I've done a couple of things that might stop the problem. But to be honest, I can't figure out what is going on. The techies in the audience know that sending the emails requires a script (program in older jargon) and a cron job to execute the script in the background. I can't find evidence of either.
The last time this happened (June of 2017), it was version 1. Since I log each email sent, the log table filled up, drew the attention of the hosting service who locked me out of the data base. Once their tech rep cleared the log table, we were back in business and the problem seemed to disappear. This time the log table is empty.
If it continues to be a problem, I will hear about it; and I will try to do something.