Thanks for the suggestions. I changed the cables, but it didn't change anything. The original ethernet cables are good quality cables, or were for their day, although they probably pre-date the 5E standard. (But, then, if the 202 is only running at 10Mbit that should be adequate, right?) The 202 is hanging off of a Gbit switch, but the run to the A* server is 100Mbit, so there is a bit of speed shifting going on. However, I don't think that is the source of the problem. Bottom line: I can always resolve the problem by backing off of using TLS -- it is really unnecessary in this environment -- but I'd like to understand what's going on. I only wish I had noticed this before I upgraded the Asterisk package; if it wasn't so hectic a time of the year, I might roll back to the older Asterisk just to see if the problem persists or goes away.
Addendum: After re-reading my own post, it dawned on me that I still had some old A* logs from before the upgrade, and a simple grep reveals no instances of "SSL_ERROR" in the logs prior to the upgrade. Thus, I must conclude that either A* 13.18.2 has a problem or I somehow didn't build it right. Still it's odd that of the three SIP connections on this 202 only the one appears to have been affected.