TBH, on face value, it sounds like sometimes you are connecting to another server (that isn't yours; and is showing the default Apache page). The only other possibility that I can imagine is that someone else is screwing with your server and temporarily disabling your WordPress site and changing your root password. Then later on, changing it all back again?!

I have never experienced anything like the behaviour you are reporting and find it hard to imagine a scenario where a TurnKey WordPress appliance could even do that. AFAIK we actually remove the default Apache page at build time.

So my guess is that you are accessing your server via domain name. And for some reason, sometimes, your domain name is being redirected to a different server somewhere else.

I suggest that check your server's IP address (when everything is working). Then, next time it happens, also check your server directly using IP address (just type the public IP in your web browser). If your site displays via IP, but not via domain, then do a ping (or use some other network tool) to discover the IP address that your domain is pointing to.

Assuming that I'm on the right track, armed with that info, you can talk to whoever manages your DNS and get them to look into it (and hopefully fix it).