The dam thing keeps messing up.

I'm just sitting here playing the xbox, or on the internet, and what happens is, first xbox live disconnects, then shortly after that, some websites stop working, then more websites stop working until there are no websites that work at all.
But, it would still say I have full strength connection, and it says "internet access".

I can fix it by resetting the router, but it happens very frequently, and it seems to be getting more and more frequent.

Anyone know what this problem is? And how to fix it?