(I apologize for making a new thread about it
here
. I really did search and search the forums using all kinds of terms, including "unable to edit profile" but this thread did not come up at the time, I swear!)
I cannot be sure of this, but I suspect the problem manifested when my host automatically upgraded my Joomla installation to the latest version (1.5.23) on or around 4/4/2011.
I am also using CB 1.4 (But it was happening in 1.3, which I just upgraded from to see if it would be fixed, but it didn't)
Ok, now I figured/found out, what the problem was.
On my host the CB-User-Edit-Functionality was not working because I was using the alias-webadress (of my host) to login to Joomla-Admin.
Editing this with the main host-adress works perfectly!