I think it's a nagging belief that's only gotten stronger the longer Matt's life has gone on. And as you said, his life can be seen often as a 'one-offs'--he meets Foggy but has to lie to him, he loves Elektra but when he affirms that he won't kill someone he loses her, he gets to become Daredevil but that almost makes him lose Foggy (and later it sort of does completely), Elektra comes back but that wrecks his life, etc, etc. He feels, I think, like he is meant to suffer and end up dying for the good of everyone else, and so he heads towards that goal full-heartedly.

This is also why I think he's not good at doing what Foggy asks of him, or requests of him--he knows one day he'll die, and he doesn't see why delaying it would help. He knows he's doomed, so he doesn't think he's going to have a long happy life, and so it's difficult to impossible for him to try to be more careful in the present-day. He also knows damn well that Foggy doesn't see Daredevilling as a 'part' of Matt so much as something Matt 'does', which is why he feels rejected and abandoned by Foggy's attitude in S2 and in the Defenders until Foggy gives him the suit--because that moment, to me, says 'I know you, you're going to be out there, that's who you are and I'll help you be who you are', and Matt's shocked by it and so happy with it.