Skype app on Android
It sounds like the skype ports are being blocked
Ask the IT staff if these ports are being blocked.
For Skype to work correctly, the following ports need to be open in your firewall:
443/TCP
3478-3481/UDP
50000-60000/UDP
For the best possible call quality experience, these ports are needed too:
1000-10000/TCP
50000-65000/TCP
16000-26000/TCP