How to convince someone to seek professional help?

I'm 19 almost 20 and I'm dating a 36 year old man. I am in university and work a part time job to pay the rent. He doesn't have a job, he sits at home all day playing guitar hero. He's extremely depressed so I cook, clean, pay the bills and the rent. On weekends I bake him his favourite cookies to try to cheer him up.

I have suggested he go seek professional help. I even said I would help pay for it. (I told him I would use some of my student loan money) He says that he doesn't have the energy to talk about his feelings to a complete stranger.

He's a sweet guy, and I feel bad for him but I am getting tired. I don't want to leave him in his time of need, but I feel obliged to stay until he can get up on his feet.

Tell me how do I convince him to seek professional help? A part of me wants to just leave him and say screw it. But I would feel like an awful person and you shouldn't leave people in their time of need right? I would feel awful if he commited suicide and I don't know if I'd be able to forgive myself for the rest of my life.