I had same problem.
I tried reinstalling application and everything, nothing worked.
If you have voice mail activated and some one left you a message
skype is trying to download messages. You just have to wait until skype signs in.
Delete the voice message, try to sign in again.
That worked for me.
i got sane prob b4....but when i download this one....now iam happy...remember: first time is signing it will take time but after that no time
I have the same issue. I deleted my Skype from E72's external memory (where I initially installed) then re-install on phone memory. It took some time to sign in but it worked! So first time after re-install worked.
When I tried to sign in the second time, it went back as before. It would try to sign in but it gives up and reverts back to skype name display. So it only worked for the first time but not afterwards.