I was transferring my Moodle course from one server to another. That was when I lost the e-mail self registration capability. I'm not sure which of the following factors contributed to the problem or to the solution, but in case others come across similar problems, perhaps this might spark a solution....
My former Moodle site was a little over a year old. --- I suspect NOT 1.9.2, but perhaps. My new Moodle site IS 1.9.2
I uploaded my old-site backup files to my new site and restored them there. Although I was rolling the course over for a new group of September starts, I didn't reset on the old course while it was on the old server -- I left that to do on the new site. So, I still had a number of students, already enrolled in the course when it was restored on the new site. Finally, I reset the course on the new server. Still, I could not get e-mail self registration to work.
I'm not sure if any of the above was a factor, but that's the context in which I was working.
I deleted all of the students from the list. Still, I could not get e-mail self registration to work.
Then, I disabled e-mail self registration and enabled as many of the other options as I could and saved the course and logged out of Moodle with those other options enabled. Then, I opened Moodle anew and enabled e-mail self registration. For the first time, I could see the e-mail self registration was enabled.
To make a short story tedious .... at last the e-mail self registration is working for me. I'm not positive what action actually made it start working, but right now I feel like my final action was one that I took a number of times earlier ... only, this time it worked!