The Skype app has to be open and displayed on the phone in order for someone to call them, otherwise if it’s in the background, nothing happens.
Skype 1.0 for Windows Phone lets you make Skype video and voice calls over 3G and WiFi, seach for and add contacts, and make calls to landlines. However, no one can call you via Skype unless you have the app open and running on your phone. Unlike Android and iOS, Skype needs to be your active app in order to receive calls as there is no background functionality at all in the app. Tango video calling service supports running in the background so if video calling is important to you then try that service out.
Even the Vita app for Playstation Vita announced for release today in the USA and tomorrow in the UK, supports background use.
Yet Microsoft are the ones who own them.