If working with him is going fine on your end (which it sounds like it is), I would stay. His issues with his program are irrelevant to you two working together in my mind.
However, as always, follow your instincts. Professionalism issues could mean many things from being habitually late to sexual harassment. If it's something like the latter and you feel unsafe and your instincts are telling you to leave, the leave.
Presumably a resident would be working with a faculty member on a project. If you're able to work with the resident without any issues and he does get kicked out of the program, I imagine it might be possible for you to continue working on the project if you're interested and it's something that you can actually do.
The goal in all research is to make sure that you do something that will lead to tangible products. Your time is limited, and it's not difficult to spend a lot of time "doing research" without having much to show for it. That's what you want to try and avoid.