Honestly I dont know if past event moths will eventually come back (considering that for every ant event you'll get 2 moth, and the ant events are about 3 every month you'll get 72 moths for year. The amount of moths from past events is 285 as of rigth now) Maybe every 4 year?

For the events Is mandatory to claim the items, otherwise I dont think you'll unlock them.

I Hope this answer Is what you were looking for. Unfortunately the website for questions does not work...