Originally Posted by Hoofprints in the Sand
Maybe you could try having someone longe you and your horse while you ride without reins and practice balance, then gradually gather them up a little at a time? Then at least you're not worrying about steering and all that, you can just focus on the balance and the reins.
^ I agree 100% with this. Lunging without reins works amazingly. It literally forces you to use your leg muscles to develop a strong seat. Holding your arms out on either side of you, also helps you to balance, without the reins.
It sounds like you are really depending on your reins to help you balance when you ride. The reins should only be used as a subtle aid to help you "steer" (hate that word, but I can't think of anything else at the moment) and to establish contact with your horse. A rider's seat is incredibly SO much more important. Focus on loosening your reins, as Hoofprints suggested, and scoop your butt into the saddle, using your inner leg muscle. (This is esp. Hard at the sitting trot -- your back needs to be straight, shoulders rolled back). If you're posting, post subtly up and slightly forward. Don't use rely on your reins to push you up. You should have plenty of weight in your heels. Riding without stirrups is also a great exercise. Good luck!