Do I give him space?

For the past month my boyfriend has been stressed beyond stressed with work, and one of the problems adding onto the stress is our relationship. He's admitted to being insecure about how he feels he isn't giving me enough and how I deserve better. I keep telling him that it's fine and happy. But he's just been so... Distant and weird lately. He normally messages me daily but I've been having to message him first otherwise he won't do it. He didn't message me yesterday, and we barely exchanged words today. When he does message me he's short with me. He'll read my messages and then not respond.

I have suggested we take a break if it's needed because I don't want to be another thing that he has to stress and worry about, but he says he'd feel like he's failed me. I don't know what else to do... He's pulling away from me and I don't know if I should just let it be or keep trying to be there for him. I used to not be stressed about us but now I actually am and it's really making me question if we should even be together anymore.... I need help, desperately.