Is this happening when replying to a mailing list which has a Reply-to address, and the latter is ignored?

https://www.mozilla.org/en-US/thunderbird/52.4.0/releasenotes/

This is not happening with a mailing list. To compound the problem, the function works with some received emails and not others. I have added images of the pertinent part of the source for the sent email and the response pane generated by Thunderbird.

Do you have any add-ons that might cause the problem? Help/Restart with Add-ons disabled (safe mode) to test. Display Contact Photo is a candidate.

I use no Add-ons. I have tried both of your suggestions in any case. Neither solved the problem. I really appreciate your thinking about this.

There are a number of Reply-to bugs, some of which may apply to your situation, but it's not obvious to me. One thing I note is that Reply-to may be ignored if the sending address is in fact one of your own accounts or identities, which appears to be the case looking at your pictures.

The sending address is one that I control but not one that is known to, or accessed by, Thunderbird. I will try a totally different address. Notice, though, that in my pictures the Reply-to address is not only ignored, so is the From address. No address is filled in. I will keep experimenting. This may simply be a bug that is very unusual and will be very hard to cure. Thanks very much again for all the time you have devoted!

In these cases, it sometimes helps to create a new profile with Profile Manager, add an account, then see if the problem remains. If it does, and you decide to file a bug, the chance of it being examined by the experts is much higher, since you have eliminated factors introduced by an old, possibly corrupted profile.