Welcome to the forum.
When Audio hardware is not working with an Adobe program, I first look at the ASIO settings. I suspect that you have already checked that out carefully.
Next step, when all setting ARE correct, and I still have issues, I install a free ASIO driver, ASIO4All, and set the Adobe program to use that. It has cleared up all sorts of issues with Adobe programs, with low-end consumer cards to some esoteric pro gear. It's probably the most often recommended "fix" on the Adobe Audition Forum.
Thanks for the reply! Unfortunately I failed to mention that we're running it on a Mac (OS 10.6.8), so ASIO fixes won't help us.
Unfortunately, that's really the only trick in my bag, and being a PC-only guy, am totally clueless on Mac's.
Maybe others will have some ideas for you.