Welcome back paintingblack!

I know this is a very optimistic approach, but can you talk to your bf about this issue? In your last post you mentioned that he is self concious enough to see the problem, so maybe you can carefully strike up a conversation about this situation and together figure out an excuse that he is comfortable with? Or even better a way to make him feel secure enough to join you?
If this is not possible, I would probably keep it vague and just say that your bf doesn't feel like hanging out at the moment. I agree that it's important to respect your bf's privacy and not elaborate on the exact circumstances.
Is your bf trying to work on his self-esteem issues (e.g. in therapy)?