Perhaps you can start with empathetic remarks on his/her bad days like, "Gosh, you sound like you have a lot on your plate. Have you ever considered talking to anyone about it?" Maybe if you can help that person talk to a counselor, the counselor could make the diagnosis.
My mother suffers from several mental illnesses. I know how challenging it can be to not get upset with the person suffering. It can totally take you over, so be careful with your decisions. Sometimes mentally unstable people find a person and really latch onto them. It is hard to not want to "fix" a person you see suffering, but there are professionals who can help.
A.