I switched from woocommerce to a different shop installed on a subdirectory for mysite.
When creating a new post mysite would crash for eithor 10 minutes or for 1 hour. No rhyme or reason.
Turns out, the woocommerce plugin was causing too many database queries. My host allows 75k per hour. When posting I would hit more than 75k. My sql database would crash and mysite would crash. At the top of the hour my host would reset the database (hence the site being down for some amount of time until the top of the hour).
Uninstalled woocommerce plugin. Now using Opencart installed in subdirectory (not part of wordpress). I put links from the wordpress site to the opencart site (the user does not see any change).
Mysite is faster and does not crash when posting, without the woocommerce plugin. I also have WPSupercache and the Cloudflare CDN working well (shopping carts don't like cache).