Was it inevitable that the League of Nations would fail to preserve the peace?

There is no way to know for sure what things in human history could possibly have happened differently.  We cannot run experiments on human history to determine whether the League of Nations could have achieved lasting peace had, for example, the Great Depression not occurred.  However, I would argue that the League of Nations was doomed to fail for two main reasons.
First, the League was arguably doomed because there were countries that were potentially quite strong that were dissatisfied with the status quo that the League was trying to protect.  Germany and Japan were the most obviously unhappy countries, but Italy was not particularly happy with the status quo either.  When powerful countries are unhappy with the status quo, they will work to overthrow it.  This will make it difficult to preserve peace.
Secondly, we can argue that the League was doomed to fail because strong countries were not really willing to support it vigorously.  The United States never even joined the League.  Other powers, like Britain and France, did not try hard to enforce the League’s sanctions against countries that violated League rules.  If a country like Italy could invade Ethiopia without the League doing anything serious to stop it, why would other countries feel that they had to obey the League?  If the major countries of the world were not willing to put their weight behind the League’s rules, it would be very hard for the League to keep the peace.
While we cannot know for sure if the League was doomed to fail, I would argue that it was.  There were powerful countries who wanted to upend the status quo while, on the other hand, there were not enough powerful countries that were willing to use their power to support the League’s efforts to preserve that status quo.
http://www.kinged.org.uk/_files/history/league_of_nations_model_answers.pdf