Hallo, I've got same problem since upgrading...
CB 1.1. Joomla 1.0.12
How can we solve it?

What can I do now? People cannot register any more, some of them contact me, some others probably just fly away from our site?
Do you think I should use old backed-up files ( CB 1.0.2) and replace new version with old one?

I am also getting this problem after upgrading from 1.012 to 1.0.13 and upgrading cb ... any fixes yet?

I'm getting this same problem with a brand new install.

Ok so if you look at comprofiler.php, around line 1015, you should see something like this:
[code:1]// simple spoof check security
cbSpoofCheck();
cbRegAntiSpamCheck();[/code:1]

if you just comment out those 2 functions like so:
[code:1]// simple spoof check security
//cbSpoofCheck();
//cbRegAntiSpamCheck();[/code:1]

Then it will fix your problem. It's just a little bandaid that you can kinda paste on there. If you're feeling really adventurous, you can check out comprofiler.class.php in the administrator/components/com_comprofiler, and look at those functions in that file where they are defined, then you can maybe determine exactly what the functions are there for (something about making sure nobody's using an automated program or something).

It shouldn't do anything bad to your site at all, and it will let people register. If you have any problems with the whole "Session expired" mess, then those functions are probably the problem causers.