Nah, the game will never delete any of your possessions in your inbox, even including any old event items you don't use during the event it was hosted in.
For example, if you still have 2 Fish Hooks in your inbox after the Sea Paradise event ends, you will still have those Hooks in your Inbox for as long as 2 months if you wanted to. But the moment you collect those Hooks after the event, they won't appear in your Inventory and will just disappear, really.
Do note that you're only allowed to view up to 1000 items in your Inbox. Once you go over the limit, the older items will be hidden from you, until you reduce your stash amount to less than 1000.