Why is my internet so terrible?

My family has used Time Warner Cable as an ISP for years now and it has always been bad. It is very fast, but it frequently disconnects me from games and websites and by frequently i mean every 10 to 20 minutes. We have tried many things and have gotten a new router hoping that that would be our solution, but it wasn't. This occurs not only on wireless computers/gaming systems, but also on the computer directly connected to the modem. Does anyone know how i can solve this problem?