Is he married or does he have kids? If either one, I'd say give up. Either of those things could be the reason he was busy and didn't get back to you right away. Plus, who wants to be a home wrecker?!
If he's not and doesn't have kids, maybe that's just the type of person he is. You could keep messaging him when he sends you messages and see where it goes. Maybe he's got something going on in his life right now can't can't devote any more time and attention to you?