It was recently brought to my attention that some sites see that behavior randomly. Jason wrote an article about it some time ago: https://s2member.com/kb-article/automatic-eot-system-option-goes-blank-why/
I still haven’t found the reason, and apparently no one has been able to reproduce it consistently in order to troubleshoot it more efficiently. You’re the first one I see mention that it happens so often or soon.
If you have a way to reproduce it consistently, then based on Jason’s article, it’d be great if you could do some testing to find what may be causing it. I’d test for a plugin/theme conflict. See: https://s2member.com/kb-article/common-troubleshooting-tips/
I look forward to your update if you can find something!