Are you using WP8.1?
I think we had a clue, but need more information
Did you try to turn off speed mode?
I can't log in to many sites after the latest update. I have Nokia Lumia 925 (so WP 8.0, I guess). It's frustrating, and I hope it will be fixed soon. Also, now I can't anymore open pages in tabs when pressing links.
It works well on win 8.1 without any problem, i use it from its beta version and didn't face any problem yet, I can login on any site using speed mode and also without speed mode, try reinstalling uc then may be your issue will gone....