Thanks for the info. I checked the default messages app for Android, Textra and Message+. They are all at the latest levels and are set to auto-update. In the default app and in Textra, I don't have any indication of a message from the group. Other than the message I received once (see original post), I get nothing. I have even uninstalled and reinstalled and disabled / re-enabled the apps and cleared the cache/ settings. None of this has helped. The person sending the texts is using an Android phone and the Messages+ app to send. The crazy thing is, when other people reply to the group, I still don't get those texts, either.
As a test, I created a group message with myself and a couple members of my family using Message+, they all received the same message I posted in my original response, but nothing after that when I sent a couple more texts to that group. I then texted the same people using both Textra and the default Android messaging app and everyone received the text just as I sent it.
It definitely seems to be related to the Messages+ app from all my testing. I have had other people say the same thing. I think it is related to having to add a "Group Name" in Messages+, but I can't test that because it is required and no way to add members and just send it with no title (at least that I can tell).
Any other suggestions or ideas?