The same problem here with the latest MacBook Air (1.8 GHz Intel Core i7). The worst part is the MBA actually turns off because of the heat. I thought the problem was my machine, but now I feel hopeless. I never imagined that the newest equipment would not run a rather basic application....
We have both a 13" and an 11" 2010 MBAs and use Skype frequently. I am yet to see either of them shut down because of Skype.