|"I use a DSL Cable Internet through Cox my Modem is a Motorola SB5101U."|
Is that even possible. I did not thing you could use ATM through Cable TV networks. I have Cox my self and they don't use DSL.
That aside, it could be poor signal to your modem. Does your connection behind the modem go through a splitter to the TV? If so then you may need to relocate you modem so that it does not or purchase an Uneven Splitter. Uneven splitters give more signal to one leg than the other. For this reason they are sometimes called Taps because you can use them to run a loop in the house. I would get two, a 6db and a 9db and play with them to see what gives you the best result without degrading your TV signal.
The other problem could be after the modem. When you lose internet does the Send and Receive LEDs blink on the modem. If the do not and stay solid then you may have a problem in your router. (Assuming you have a router.) Try pinging your router when the internet goes out. If you can not ping it then look at the LEDs on the router and let us know.