I tried the method that Fyrewolf5 mentioned, of re-synching myself with the server, then the method that Kajex suggested. I'm not sure which one worked, but now a friend can join me reliably so far. I'll get more friends to test it, but it seems like it's been fixed.
EDIT: Nope, it hasn't been fixed. I'm still getting the same issue with another friend. I don't know what to do anymore.