If I don't collect a prize from an Event before the end, do I lose it?
Yes, you lose it forever.
Events have a duration. In that period you must not only win those prizes, but also claim them (by clicking on the "Claim" button next to the prize won). If you don't do it, you won't be able to claim that prize and you will lose it.
Keep this in mind and, although it is difficult to happen, if you see a red dot in any Pass, look at it because you will have gained one more level, and it can give you a prize. Claim it!
But it also happens in the exchange of plans in the design challenge. Don't let it slip away! Exchange your plans before the end of this design event.
(*) Contributed by Atlantis