I completely agree with this judgment, since the Manchurian and Abyssinian crisis did in fact fatally weaken the League of Nations. One could almost argue that both crises led to the destruction of the League, as they could be seen as the first links in a chain of events that led to the Second World War, which was to be entirely prevented by the birth of the League of Nations. The League proved to be incompetent, as it could not deal with both crises effectively. For instance, It was powerless against Japan (initiator of the Manchurian crisis) and Italy (initiator of the Abyssinian crisis), due to the league having no army to enforce its policies (It could only impose sanctions and a ban from the League), hence weakening itself, and ultimately leading to its destruction. However, it is also important to identify the weaknesses of the League that existed prior, as they may have guided the League into its fatal state.
The devastation of the First World War horrified countries worldwide, with people living in fear and anguish, hoping to never encounter such an event again. To their salvation, the League of Nations was created, promising to maintain global peace and to prevent a Second World War. The League was established in 1919, under the sheer will of President Wilson, who wanted the League to be seen as a type of 'World Parliament'. Here, international disputes or interests could be discussed formally, without the violent use of force. He also hoped that the League would stop all wars, improve people's lives and jobs, improve public health, put an end to slavery, persuade nations to agree to disarmament (as this would make war impossible) and to enforce the Treaty of Versailles - which acted as a peace treaty. Countries were in favor of these ideas, resulting in forty-two countries joining the League initially, which ascended to around sixty countries in the 1930's, strengthening the League's international power. However, Even though the intentions of the League were positive, it failed miserably, as the League was incapable to deal with the major international disputes as it promised it could. The late 1930's put the League's true power to the test. During this decade, there was a world-wide economic Depression, where Japan was majorly affected. Japan's government failed to deal with the Depression, and thus decided that it would have to occupy the whole of Manchuria (In China) as an only solution. This would have enabled Japan to have access to the region's valuable resources of coal and iron in an era where it was already difficult to purchase these vital raw materials. Japan, to it convenience, was soon provided with an opportunity to invade Manchuria. On 18 September 1931 a bomb exploded on the railway close to Mukden, where Chinese and Japanese soldiers were stationed. Japan instantly blamed on the Chinese, which instantly provided the desired excuse for Japan to occupy Mukden and the entire southern Manchuria. China - being a member of the League of Nations (Japan was too) - desperately plead the League to help. Due to the weak organization of the League, the response to China's problem almost took an entire year. However, in response the council of the League asked Japan to withdraw its back to the railway region in Mukden. However, Japan decided not to do so, and turned Manchuria into a Satellite state of Manchukuo. Shortly after, Japan left the League of Nations, as it had no more further interests in the League. Its essential trades were offered by the USA; therefore the Leagues policy of sanctions was ineffective, as the USA never joined the League of Nations, giving Japan no economical punishment. The Geneva Protocol  was never ratified, therefore the League did not have an army to take military action, and war was absolutely out of the question. Britain (Head of the League of Nations), however, did not urge to take action against Japan, since neither the Government nor the people desired to fight a war purely without central British interests. Therefore the league was powerless in taking action against Japan, fatally weakening it. Some members of the League noticed this failure and realized how ineffective the League of Nations really is, and thus left the League, weakening it further. The Great Powers of the League  were unwilling use force against Japan, because of the self interest of a Great power (Britain) in Japans actions. Britain had secretly supported Japan and shared sympathy with Japanese action in Manchuria. And similar to Japan, Britain had some commercial interests in China, which were threatened by the ongoing chaos and civil wars. Therefore Japans invasion seemed to restore order to this issue, pleasing the British. This weakened the League, as the League could not take any action against Japan since a Great Power of the League secretly supported its actions.
A few years later, in Europe, another fairly similar crisis began. Italy was trying to distract its people from the economic Depression, and therefore wanted to erect a large empire in Northern Africa. By invading Abyssinia, Italy would not only be provided with land for Italian settlers, but also connect Italian Somaliland with Eritrea, therefore putting most of the "Horn-region" of Africa under Italian rule. Mussolini  , by 1932, began his plans to invade Abyssinia, and On December 1934 Italian forces began to clash with Abyssinian troops and shortly after, in October, the long-desired invasion of Abyssinia began. Mussolini had no doubt that neither Britain nor France would intervene with his plans, giving him the perfect invasion plan and opportunity. However, while the French Foreign Minister, Laval, was promising Mussolini a free hand, Britain tried by all means necessary to find a compromise. Britain wanted to offer Mussolini a territorial compensation elsewhere or negotiate an arrangement which would give Italy effective control over Abyssinia avoiding a "Formal Annexation". This already suggests that the Abyssinian crisis fatally weakened the League of Nations, since the League changed its policies (a Volte-face) when France supported the invasion and mostly when Britain offered Italy other suggestions of gaining territory. The policies of the League were collapsing and with it the league.
Italy neglected the offers suggested by Britain and pursued its invasion of Abyssinia. In 18 October, the League condemned Mussolini and imposed a ban on weapon sales along with a gradually ascending program of sanctions. This had no effect, hence rendering the League powerless and fatally weakening the League. In the meantime, Britain and France were searching for an alternative compromise to Italy's invasion. Pierre Laval and British Foreign Minister, Sir Samuel Hoare, created a secret plan that may have been suitable for Mussolini. It involved giving Italy control over only two-thirds of Abyssinia. However, the plan was secretive and illegal and it somehow leaked into the French Press, which ultimately resulted in the resignation of Sir Hoare and the dropping of the plan. In addition, the League did not ban any oil exports to Italy, which was a vital trade, and the Suez Canal, where Italian ships could drift through, was refused to be closed because Britain feared war. Mussolini had no obstacles in his way and by May 1936 had overrun Abyssinia. Hence no action was taken against the invasion of Abyssinia, weakening the league, as it was powerless and ineffective in stopping the invasion. Both Powers Britain and France also feared the diplomatic consequences of alienating Italy over Abyssinia.
Not only did the Abyssinian Crisis fatally weaken the League, but also provide Hitler with an ideal opportunity to remilitarize the Rhineland and recreate an all-powerful Nazi-Germany. This was to be entirely prevented by the League, as the Treaty of Versailles did not allow Germany to have an army, since she already began the First World War. Furthermore, the Franco-Italian friendship was destroyed and replaced by the Rome-Berlin Alliance (Axis), which enabled Hitler to absorb Austria in 1938 without Italian opposition, creating an even more powerful Germany. The "Axis" also threatened British and French communication in the Mediterranean, which would ultimately weaken the potential in future response, under German or even Japanese aggression. Soon after, Germany gathered sufficient power and the Second World War was inevitable. Overall, this fatally weakened the League of Nations and ultimately led to its destruction, because Germany was able to rebuild and become a strong Power again which later on led to the Second World War, where both were to be entirely prevented by the League. Members of the League realized ineffectiveness of the League and instead left the League to prepare for war, fatally weakening the League as it no longer had loyal members. The League created more problems than solutions, weakening itself, since it should have been in control which it was not. Instead of finding an effective solution to solve the crisis, it somehow found a way to damage itself and put itself under risk, ultimately destroying it.
The Manchurian and Abyssinian crisis did in fact fatally weaken the League of Nations. One could almost argue that both crises led to the destruction of the League, as they could be seen as the first links in a chain of events that led to the Second World War, which was to be entirely prevented by the birth of the League of Nations. The League proved to be incompetent, as it could not deal with both crises effectively. For instance, it was powerless against Japan in its invasion of Manchuria, since the League had no army to fight against Japanese aggression. Also the self interest Britain had in Manchuria provided Japan with protection, therefore fatally weakening the League. In the Abyssinian crisis, the League was powerless once more and could not take any action against Italy as they favored Italy (to support against Nazi-Germany) rather than the loss of Abyssinia. It tried to implement sanctions and a ban on sales of weapons, but this had no effect on Italy. Due to the failure in Abyssinia, Germany was capable of rebuilding, and thus ultimately leading to a Second World War. Members of knew that a Second World Was threatened, hence fatally weakening the League as it no longer had loyal members. The Abyssinian and Manchurian crises fatally weakened the League of Nations and ultimately led to its destruction.