After more than a year of dealing with this problem I spoke to an agent in INDIA, Hari, who solved my problem in a 15 minute phone conversation.
The issue was that the upload speed in my modem was set too high. I have an Actiontec 984 WMV. He sent me to the status page to read him the download and upload speeds. The upload speed was 1.125 mps. The told me the highest speed my line was able to handle was 1.124.
Of course this sounded nutty to me, but I followed his instructions, turning the modem off for a few minutes. He made two tries, and afterward, the new upload speed he set in the modem was 1.107 mps. I am happy to report that instead of resetting from 7 to 10 times in the intervening 20 hours, MY SYSTEM HAS BEEN ENTIRELY STABLE WITH HIGH SPEED AND NO RESETS.
Many earlier phone contacts had resulted in about 5 new modems, none of which ever had fixed the problem. They tried to charge me for a few of them. Overall the lack of expertise in the Verizon support network is rather appalling, but this hint might help some of you find an answer for this problem.
Glad to hear it is fixed. Bummer the fix didn't come sooner. The values the agent mentioned may sound nutty, but the concept when provisioning is to build in some head room so the line can tolerate noise. If the connection operates at the max attainable rate, there is little room if any for noise, and hence the drops.