After every cron job, the Media tags in WYSIWYG markup change to https upon a robot crawl
If you don't want HTTPS, simply turn it off. And if, for some reason, you want HTTPS links to still work, you should redirect HTTPS to HTTP - but that's out of scope of this site. Just never leave https on without proper certificate.

That said, you have some serious bug in your caching configuration, and data you provided is not enough to identify it. Luckily, there is no need to do so.