I think the title is misleading. The OP's BF knows he stinks. He has lost a job because of it even. He knows his GF is unhappy about it. This is not about alerting him to an issue he would otherwise be oblivious to. This is about getting him to do something about it. Therein lies the problem. The OP cannot do anything FOR her BF. So she needs to decide whether she can stay with him if he continues to do nothing about this known issue.
He processes the words just fine when it's brought up (like when his former boss confronted him and he came home and cried, he obviously understands what's being said), but he doesn't retain the information. Every time it's mentioned, it's like it's the first time and he seems surprised to hear that it's a problem. He's not generally a dirty person, this is only an issue when his depression is at its worst, which luckily seems to only happen around every year and a half or two years, and he is diligent about getting the medical help he needs at that point. This is just not something he seems to process as being a problem. I think he just doesn't realize how bad it is or how it comes across to other people because he's got so much other stuff on his mind, it's just not a focus for him.
I really appreciate everyone's suggestions. I'll definitely be calling his doctor. I've tried to do it in the past, but I never got a call back, but I'm going to be much more persistent with it this time. He's gotten so upset when I've tried to be very frank with him, but maybe some different phrasing will work better. I think maybe the suggestion to actually draw him a bath and start helping him bathe may work out well. At that point, it's a severe enough reaction that it would be pretty hard to forget everyday that something is wrong, but maybe it will come across as less attack-y and help him get back into the swing of things.
Good luck to you too, CLD. It sucks to have to watch someone you love go through this and to not really be able to step in and make it better.