Just got an update on the ticket for all the database issues.... I'm not much of a linux guy, but seems to make sense. Here's to hoping!
While checking I can see some exim stat queries taking too much time to complete (around 1200s) and suspect this eventually putting mysql to an unresponsive state. I have now truncated the Exim stat database and enabled mysql monitoring in cPanel. Please keep monitor this and let us know if you still see any downtime with mysql.