My websites go offline several times a day. I can still go in to my WHM in cpanel. I hit the restart apache button and everything comes back online in seconds.
What could be causing this?
There certainly seems to be some memory corruption going on. If that corruption only hits the children your main apache process might survive... provided you don't use something like the threaded process model which shares the code between all apache processes. Your question is tagged both apache1 and apache2, even for this first paragraph I choose to believe you're not running the ancient 1.x version... :)
If the main process (with the "old" but trusty pre-spawned child process model) is corrupted it might be hardware - bad memory or actual corrupted code on your disk... else a child process could theoretically corrupt the parent process as well. Check your modules as well, since the corrupted code could be there.
Whatever the reason, I hope you keep your apache up to date - there are quite some security holes being fixed on an almost daily basis, and since webservers are the #1 attack vector that can't be stressed enough. There's also good advice about how to harden your apache configuration, even from the apache project itself.
Btw. the phpmyadmin attacks you are seeing are probably not an attack on your server but an XSS attack on some other server. Anyway, this list should help you if you actually run phpmyadmin.
In my opinion
Some other service is also trying to use the port of apache. try to find that service and stop that service.