What should I do if my wife has manic depression? Is it possible to stay married?

Bipolar. Sure it is. As long as she has good support system, good therapist, and complies with prescribed medications if she is on meds., prognosis is favorable.
He has to want it. Your wife has to want therapy and medication, and all you can really do is encourage her to seek both and engage deeply and meaningfully in the therapeutic process. You simply cannot do it for her, much as you'd like to. You can either be her husband or her therapist. You cannot be both, and even though you want to see her get better, trying to be both simply will not work. Yes, it is possible.