Thanks to Keath for figuring this one out for me (and all of us):
My e-mail address changed since I signed up for the permanent-number pseudo-event back in February, so I dutifully put my new e-mail address into my profile. But then the e-mail address the system associates with my permanent number no longer mached the one in my profile.
I can't edit my permanent-number entry, so I set my profile back to its old value and could register just fine with my
number. Of course I won't get my any confirmation mail, but at least I can register! Flip-flopping my profile is clumsy, but it works