After every cron job, the Media tags in WYSIWYG markup change to https upon a robot crawl My site doesn't use https certificates. 

The Media WYSIWYG markup changes the images protocol and caches them as https and therefore they don't display as there is no certificate on the website!! 

The only thing I could do is re-save the affected pages if I spot them and then it's all good until another robot crawls them again in https after a cron job, which will revert the Media WYSIWYG markup from http to https and we are back to square one. 

What is the solution for this?

Can the Pathologic module solve this?
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.