Skype is officially blocked in Dubai. A two second Internet search reveals this and its even stated on their website. People can get around this by using proxy servers and VPNs. Indeed, even some hotels, recognising it's good for business, get around it by routing traffic through foreign VPNs. Appears to be a loop hole in that proxy/VPNs are not banned by the state.
Similar problems for most expats living in places that look good, pay good but offer very little freedom and quality of life (if you are prepared to look beyond the superficial).