1998 Chevy Cavalier transmission is staying engaged

1998 Chevy Cavalier mileage: 88,000. After the car has been driven 20-30 minutes, when slowing down or coming to a complete stop it feels as if the transmission is staying engaged, rather than coasting. If you shut the car off then immediately restart, it will stall when shifting into gear. After being shut down for ten minutes or so, it works again. I also noticed once it reaches this point it auto shifts very roughly. Thanks in advance, for any help you might provide. P.S. I had the transmission serviced, and it didn't solve the problem.