On the iPhone, iPad and other iOS devices Skype has a “Go Offline” setting which can be found under Settings > Skype on your iOS device.
What does the setting do?
It was added at the end of 2010 by Skype to allow you to specify how long Skype should run in the background after you have switched to a different app or your device locked.
You can specify immediately so Skype would logout once you switch to a different application or never so that you would always stay logged in. Alternatively specify the period of time that you want to stay logged in for.
Leaving this setting on Never is not recommended if you want to preserve your iPhone or iPad battery.