I've had very few issues with Cox internet myself. Been pretty rock stable for me.

I was having a similar problem as you about a year ago, and come to find out it was the modem that I had. It was a very old Toshiba, one of the first ones they were issuing. I went out and got a new one and it's been great ever since. I think I've had to reset the modem once in year since I got it.

Also, do you have a router? It could be crapping out on you too. Don't automatically suggest that it's the service going to shit.