I’m out of ideas and these Security Log entries don’t really give me any clues sorry. I was hoping to get a response like “I did troubleshooting step X and the issue was no longer occurring”. Uninstall BPS and try another plugin instead.
BPS removal steps:
1. Activate Default Mode on the Security Modes page.
2. Use the Delete wp-admin .htaccess feature on the Security Modes page.
3. Deactivate and delete BPS on the WP Plugins page.
4. Go to WordPress Settings >>> Permalinks and resave your Permalink Settings.