There is not currently a way to prevent items from being purged from the deleted items folder. Nor do I believe there are logs that will show when a user deletes an item.
Your conversation in the comments brings up some good suggestions though. In order to gain visibility for other users and the development team, it would be best to have these separated as Proposed Ideas. This will allows users to vote and share their feedback as well. I'll good ahead and change this thread to an Idea for you.