Does H know how much you "need" him? Maybe it would help him to save face if he came home because 'you' need 'him' rather than the other way around.
Perhaps you can just tell him you want him around. You need to have him near you more. His roommate certainly seems to need him, and he already has let you know that he needs more emotional availability from you. Is this what he is hoping for? That you will beg him to come back so he feels needed?
