Prizes expire 30 days after completion, if you do not redeem them.
You may also notice that an incomplete prize puzzle has moved to the Expired tab -- if that is the case, that means that prize has run out of stock. There should be text at the bottom of each prize listing that says "X Prizes Left!", which lets you know how many are in stock for that prize.
We'll be working to add more prizes as the stock runs out!