They remain in place and become part of the stadium.

Right now I am on level 5 and have a level 3 stadium (small town stadium). I started with 7000 seats. After the small seat upgrade, I had 8500 seats, then the medium seat upgrade to go to 10,000 seats, then the large upgrade to 11,500 seats. I'm currently upgrading to medium town stadium. It takes 3 days and I'll have 13,000 seats. The seats don't disappear b/c the medium town stadium has 13,000 seats.

The upgrade from small to medium town stadium takes 16 days (like all stadium upgrades) and adds 6,000 seats. Doing seat upgrades, 1500 seats at a time, allows you to take advantage of the increased ticket sales every 4 or 5 days and you still get 6,000 extra seats when the upgrades are finished (in 16 days).