if you say you are rebooting the modem it can be your modem. Unless you are getting confused with the router as the modem.
I have TW and actually if you tell them that your internet keeps going in an out they will come and they will replace your modem
I agree that Time Warner works hard at trying to solve issues but mine keep happening anyway. I got there supposedly "best router" new modem etc. but my connection gets interrupted. It seems to happen more during the times of day that a lot of people are online. I'm wondering if Time Warner needs to upgrade THEIR equipment to deal with increased usage? I know nothing about the details of this stuff so this is just a guess. If anyone knows if this could be the problem...let us all know