|That's the most unusual thing I've ever heard of. A piece of software causing a piece of hardware to reboot.|
You're absolutlely sure your router is rebooting?
Test this and report back.
To test, I would simply start a continuous ping from my PC to the router and then I'd run Skype. If the router continues pinging for the duration then it's not likely it's rebooting.
If it doesn't stop pinging, repeat the test only this time run a continuous ping on some server on the internet (example: www.google.com)
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.