Car/transmission problem

I have an auto question for you…I have a 2001 Hyundai Elantra gls Wagon (automatic transmission) and lately I have been experiencing some problems. The main problem is that if I have been driving it for over 20 minutes or have been going up and down large hills, I’ll be going 60 and the car will downshift and will get stuck in a lower gear. It will stay in that lower gear until the car is turned off. Once it has been turned off, even if only for a minute or two to “reset”, and turned back on, it will run fine for another good while until it feels like it and then it will happen again! The car also bucks sometimes when you try to go too fast too quickly or going up and down hills. Can anyone offer any ideas or suggestions as to what may cause this type of problem?
Thank you!

I would check out www.hyundai-forums.com

Scan the threads in the Elantra forum for ones dealing with transmission issues and I bet others have had the same problem.