A week ago I replaced my Linksys cable modem with a new Motorola SB5101U (HW rev 1, FW rev 184.108.40.206). My internet performance immediately stabilized and subsequent calls to Cox confirmed that there are no modem resets.
The 5101U firmware has a logger (yes!), so I can get a feel for what's happening on my end. After some initial hiccups in partnering up with Cox, there have been five non fatal incidents over the past 8 days and no indication of any resets. IP performance continues to be solid.
I consider my problem solved. This thread should be closed.
ps: Thanks again to Emerald for his WRT information. If my router ever goes haywire, I'll consider that option.