For the longest time, I would play this game and my car would randomly stall out if I used a button for accelerate (it doesn't happen when using the right stick). I thought my controller had a problem with analog drift, but I eventually found out that this game uses the rarely used and clearly ill-conceived pressure sensitivity of the face buttons. For maximum speed, you have to press the X button insanely hard, or you'll end up gradually slowing down.
The solution? Use a PS1 controller, which doesn't feature analog buttons. You'll get maximum speed all the time, which is obviously what you want.
http://terosclassicgaming.blogspot.com/ - Watch me beat "SNES Biker Mice From Mars" http://www.backloggery.com/tero - My backloggery