Well, as long as you have your .sav file (which, I believe, contains your saved game data; it should have the same name as your actual ROM excluding the file extension), I believe your saved data will be completely intact and you'll be able to continue wherever you left off regardless of what emulator you are using to play it.
Snes9x is my personal favorite for emulating SNES games; I'm afraid I lack the technical knowledge to know exactly what might be the problem, but I can suggest another good emulator for you.
ZSNES Home Page - About ZSNES
I would be lying if I said I didn't find using it just a bit uncomfortable, but you might want to try it out anyway and see if it fixes any of the problems.