That typically means you're hitting POST input limits, broken HTML in one of the tabs, or a FORM element is embeded inside profile edit. How many fields do you have and are you using a lot of field group fields? If you're using Custom HTML fields be sure your HTML is valid and you don't have an unclosed tag somewhere. Be sure you're not trying to do something like render a tab inside profile edit that doesn't belong there (e.g. gallery tab or field, etc..). Does frontend profile edit save fine?

So you can save users in backend, but only if logged in as super user? I assume your issue where it's failing is with an administrator? This likely means something critical is not available to the administrator user or something is available that's breaking the form as described in my previous reply. Is frontend save impacted in any way or is this entirely impacting backend?

Ok, and editing that same user from backend while logged in as that same super user doesn't work? Are there fields available in backend that are not available in frontend? Are you using CB Auto Actions to act on any profile update triggers and if so what action types are you using?