I had the same problem. However, I wish to differ with the other guys. The syncying problem is not with MPEG it occurs in all formats. The problem is if the original audio had a bump, cut or any disturbance any other new layer you try to sync will lose sync start from the point where there is a problem in the original audio. Remember this problem could be any of bump, cut. Solution, play you original or audio you are trying to sync and check to make sure there is no bump, cut or anything that cuts continuance of your song or audio.

If other than this you naturally have problems with editing MPEG natively use one of MainConcept products : http://www.mainconcept.com/index_flash.shtml. I hope this helps.