Recently I ran into this issue as all of a sudden my Skype microphone stopped working. I tried to re install it and that doesn’t work for me. Later I realized that I have recently updated my iPad to iOS 7 which could cause some privacy settings.
So I looked into settings and found that my micro phone setting for Skype were blocked. Here is how we can un block it again
Go to Settings > Privacy > Microphone > Skype
Hope this helps for users like me..