Are you able to maintain a text message conversation with your Skype? Does it disconnect only when you try a voice or video call?
I have used Skype version 126.96.36.199 on WIndows 8 on my Aspire V3-571G for the last 3 weeks and the only way I have experienced disconnects is by moving the laptop out of range of the Wireless station. Even then Skype just drops from video to voice and then to text message only, as the WiFi signal gets weaker. Otherwise it works for me even calling people on the same LAN, only once it disconnected when the other party's internet dropped. Does Skype's Echo / Sound Test Service work for you?
Could you give details of your system, laptop model, type of internet connection, Skype version, anti-malware and firewall settings?
I recommend installing the desktop version for Windows 8, see my reply above. I have seen several people having problems with the Metro version. Your laptop is the same model as mine, with Windows 8 pre-installed. I checked my McAfee settings and it gives full access to the Skype program at C:\Program Files (x86)/Skype/Phone/Skype.exe .
I just re-tried the Metro version that came pre-installed on my V3-571G and it again failed with a message about no connection. I consider this an error of the Metro app because the desktop version works fine with my WiFi connection. Speedtest.net is reporting download of 5.6 Mbps and upload of 0.69 Mbps which is good enough to handle video calls.
Check what Task Manager shows under the Performance tab, WiFi section: make sure there is no other application overloading the wireless connection.
Yesterday I installed the skype version (1.1.someting) came along with windows and installed desktop version and, eureka, its working perfectly and I had a video chat for almost and hour with out any interruption.