It sounds like there might be a problem with the profiler not liking the two different ways SNES9x deals with input. If it can map the keys, it's using directInput, but it seems for some reason it doesn't stick with that once emulation starts. Maybe it's trying to keep controls exclusive to the setup screen..? Without having a similar controller myself, I can't dig into it very far, but it's an odd problem.
A workaround is to use a program that translates button presses into keystrokes. If you grab the utility 'Joystick 2 Mouse' you can (with some effort, admittedly) remap all the buttons to the keyboard and use it that way. It takes some doing to figure out how to work the utility, but it's invaluable. I use it for DOS games through DOSbox as well, and it works like a charm.
Here's a link: http://atzitznet.no-ip.org/Joy2Mouse3/