Having the same problem with my iPad 2 and iPhone 4 both running iOS 5. Skype goes offline by itself and as a result lots of incoming messages/calls are missed.
Since there is a long silence over this, i can't help but start thinking that this is rather a political issue. I am a software enginer for quite a long time, and from my expirience it would be nonsense not addressing such a sirious problem in months. This whole situation looks like either Apple is trying to make people start using FaceTime or Microsoft pushing towards WP7. For myself, I rather believe the former because despite Microsoft having done a lot of stupid things lately this one one would be a shere stupidity that is in fact pushing people to switch to Android (unless Skype also becomes unusable on Android).
I found out that skype won't go to offline when only 3g is connected. But when wifi is connected then skype shuts off. Amazing, how hard can it be to make skype shift from wifi to 3g and back without going offline, but now.
Apple, Skype little effort, please
I got my problem upgraded to tier two with a promise that they would respond to my issue. That was last week. I'm going to wait a week and then email the head of the app development department.
Did someone answer this question? Have have you learnt since?
It's been more than a half year and I am still having this issue... Does anyone know something?