Some sites randomly hang for 2 to 5 minutes at random times of day. No clue what is causing it.

I have about 260 sites on my cpanel server. About 3 months ago a client contacted us to tell us they have Uptrends (server uptime monitor) on their site. And randomly they would see their site go offline or not respond for as short as a minute or as long as 10 minutes. When this happens, it doesn't affect all sites, so I thought it might just be their site. However, I put a monitor on about 10 different sites and they all do the same thing. Never at the same times of day, and one might hang but others are fine. Can anyone point me in the right direction where to start looking into this?