I’m normally a helper type but experience has taught me that manipulative users can be fended off with polite blandishments like “I’m sorry to hear that” or “Gee, that’s too bad.” When it comes to them, “is there anything I can do?” has been stricken from my vocabulary.

And like you, it takes only so many rejected (or cancelled!) invitations before I’ll stop extending them. How many that is is loosely based on reciprocal invites.