Update: I have tried a few different power cables, ethernet cords and outlets. I am still experiencing disconnects. Also, I plugged my computer directly into the modem; removing the router from the system. And I still disconnected. So it's not the router. I will continue testing some different cable configurations just to be absolutely sure.
Also, this thread seems relevant to my situation: http://forums.cox.com/forum_home/internet_forum/f/5/t/477.aspx
and the solution to his problem:
dubyadaCox technician came today and said that he sees this problem once a week - the new Docsis 3.0 modems "range" to different frequencies when more bandwidth is detected on another frequencies. During this "ranging" the signal drops. He said it happens with all brands of cable modems.
The technician said that the "engineers" back at the office can "fix" this. He said he didn't really know how. I asked if it was essentially locking the modem into one frequency, and he said yes. He checked the signal, as he had to do at every visit, and said I had a good signal. He took my information, said he'd be glad to call me back and let me know when "she" back at the office "fixes it". I appreciated that gesture at least.
I'm not sure what/if anything to believe from Cox, other than they seem incapable of delivering clear information to the general public regarding their troublesome service. Instead of treating cable signals like "magic" it would make more sense to deliver clearer information, so as to remove superstition and prevent silly things like me buying a new cable modem and spending hours on the phone with Motorola to fix mysterious problems.
Can you try locking my modem into one set of frequencies?