I think he sounds like someone who isn't very assertive and has a problem with saying 'No'firmly. Because all his behaviour suggests that he is trying to communicate that he does not want a relationship with the OP and is trying to let her down lightly, but she is not listening and is in fact putting a lot of pressure on someone with MH issues to be her Perfect Boyfriend.
SleepyDopeyGrumpey, what you would be best off doing is walking away from this man, making a firm promise to yourself that you do not date or engage in any type of sexual/romantic encounters for a whole year, and then you spend that year doing some work on yourself, maybe with the help of a counsellor, to fix your boundaries and learn the lesson that it's fine to be single and that no one owes you a relationship.
There was a thread a bit like this a year or two back, when everyone started off saying what a bastard the bloke was, and it gradually emerged that the OP had been told by him that the relationship was over and that he wanted her to move out of his house (in this case she had a house of her own so he wasn't putting her in the street) but she wouldn't leave and kept wailing on about how much she loved him. This man was bringing a new partner home, going on holiday with the new partner, and the OP still wouldn't move out of his house. I think it ended up with him having her physically removed by the police and taking out a restraining order (and there were still some people going, what a bastard, how could he be so cruel?). Mind you don't go the same way, OP.