I too have been having the same problem. It only takes an hour or two before my internet stops working despite a connected status. At the risk of being berated for not providing helpful information (I'm far from being a computer expert), I thought I would pass along a website that I discovered. I signed up for this hotfix and was told I should expect to receive it in 8 hours. I hope it works because rebooting every hour or two is just not a satisfactory solution.
After you configure Internet Connection Sharing in Windows Vista, the network connection stops working after one-to-two hours