I think the source of this reported problem has been found, and happily fixed (the preliminary results are promising).
Basically I needed to find some way to get the backups to complete reliably so I started a 20 count ping job a minute before the rsync job (actually an rsnapshot job which connected twice) which did allow the backup both backup connections to work (where previously just the second one connected reliably). In checking the logs for the backup status, the stats from the ping job were also there and these logs showed some dup ping packets on a fairly regular basis as well as some non-answers. As I was then able to get the same inconsistent ping results from the gateway itself (the "inside" address of the cable modem) I asked the ISP (Comcast) to replace the cable modem. They were fine with that suggestion and the replacement went in today, and I am so far not able to reproduce the inconsistent ping results to any of the /29 address, including the gateway. I'll know for sure once I stop the ping job and the backups still run reliably. Thanks to all, Chris