So why is he asking for money all of a sudden, when she's already 'gotten him next (last) time', several times over?

Actually that was never implied in her post... She said she paid for things, but not exactly that he was asking for them. Then when she gave the example of bringing coffee, well, did he ask her to? Or was it an act of good will / kindness. He had debts, and just started a new job, it doesn't sound like he's exactly flush with cash yet. He wanted to do something nice, within his ability to do something nice, so he offered to do the legwork and pick up the bagel for her... but again, maybe he's not flush with cash, and while he wanted to do something nice, the legwork, he didn't feel like he could exactly afford to pay for her bagel, and as she was going to get it anyway, he probably didn't see it as being much of an issue.

You can't hold gifts you give people over them. That's not healthy, in any form of any relationship, friends or otherwise. A gift is a gift. If you're trying to influence someones actions with them, or hold it against them at a later date, it's not a gift...

That being said, and I've made a few posts in here, I don't think her annoyance is petty. It's perfectly understandable. But he had debt. I don't know how long they've been together, but it sort of sounds like he's always had debt, and maybe always been a bit broke, it sort of sounds like she knew this going into the relationship, or at least has been aware of it for awhile and has worked around it because she cares about the guy. Now he has a job, great, but again, does he have he necessities in order? I've been broke before, and had debt, and not had full time employment... It took me awhile to recover, and I found myself in situations similar to OPs boyfriend. I wanted to at least try and do something to make up for my finances, so I would offer to pick stuff up for people, or whatever, but often ya, I'd need the cash to do so, I was just trying to save them a trip and show that I do give a damn. I felt bad about it, but ya, I was trying to do whatever I could to make up for it...