I had this problem as well after using CCleaner's registry cleaner. The modem lights would stay lit but the internet would go out for ~ 20-30 seconds, maybe 10-15 times a day. I reinstalled my NIC drivers, direct connected to bypass the splitter, reset my modem, disconnected the router, reset my modem a million times... nothing. Did start>run>cmd>ipconfig /release /renew and I believe it fixed that issue however I reformatted that day so I didn't give it much time to test.
you can also try start>run>cmd>netsh winsock reset catalog
I believe you will need to restart.