Hello, hmseb.
Did you use any sort of custom queries on your page? Something you added to functions.php yourself? E.g. some heavy qeruies dealing with a lot of tables or something similar? > Could point to programming errors or just some queries that are too intense or too slow.
Could you run your site (for testing purposes) on a different theme and does the error still occur? > could narrow it clearly down to some theme error.
Does the error occur if you put the site into maintenance mode and lockout every public access at the time the server usually goes down? > could point to to some internal error not connected with external user access or access by search engine crawling meachnisms.
Just thoughts.
Hope you find the cause.
Regards,
Karl