Is it possible you could help him fix up his resume? At least to help him feel better about it. If I'm right you have a job in which you have to communicate with other professional regularly and perhaps can use it to spice up just the wording and layout with him. Someone I date once had only vacational training and he felt very anxious about written communication so I helped him with his resume. (You never guess it by my typos/grammar on here, but my job is mostly communication)
That's so frustrating. Been there, definitely. Do you think there's something he's avoiding? Being a grown up, taking things to the next level in your relationship, something like that? On the other hand, I know how hard it is to do somethign that makes you feel stupid. And if you have a fairly sustainable situation, it all just gets easier to put off. So maybe there isn't enough of a crisis situation for him to feel like he has to fix it right now. Is he usually more of a planner? Or more laid back?