No websites do not loose page rank when they expire. A Domain can expire, go into redemption period, and the same domain owner can still pick the domain up in the redemption period. The domain is expired before it goes into redemption. I have seen this numerous times and the page rank is not lost.

I have also seen domains expired, picked up in auction, and sold back to the previous owner…. and you guessed it the page rank remained.

The problem is if you change themes or place parked pages – this will loose rank.