I'm having the same exact problem. Here is my thread: http://forums.cox.com/forum_home/internet_forum/f/5/t/1701.aspx
It has been really frustrating dealing with Cox support with this issue. The first Cox technician that I called for this problem arrived and left my house within 5 minutes, and then closed my support ticket.
The next technician replaced all of my cables and verified my signal levels were perfect... but the disconnects still occurred.
It is really difficult to get Cox support to acknowledge or diagnose the problem, let alone do something about it.
In my town the only options for internet are COX and AT&T DSL. So the only realistic solutions I've found for this problem are:
1) Move
2) Get DSL
3) Wait for Google Fiber