If the engineer was "busy in another part of the DC", I doubt having a monitoring / management faculty look over your server help. The best monitoring in the world may be unable to get a datacenter that is always "busy" to respond. I personally would recommend looking for a new provider.
24x7x365 (5 minute interval) Server Monitoring with Reboot
If your server is down, we will follow your instructions to reboot it by either contacting data center or accessing reboot port.
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We've used them before, and they know what they are doing. They offer full management with monitoring for 30$ or monitoring only for 10$.
Personally, I enjoy the monitoring that Liquidweb provides, as if your server becomes unresponsive, we're notified within one minute of it happening, and they are already on their way to walk right out to the data center and reboot it. Of course this would require moving to a different data center, but if that is not a choice, PSM is your best bet
Don't put a bandaid over the problem but fix the root problem. Why is your server/apache after time giving up or failing? Are you running out of ram? What is causing it to fail, fix the issue not the symptoms.
A stable server should be able to run without shutting down for very extended periods of time barring reboots for kernel upgrades and other such security maintenance windows.
I agree with Michael - you should be careful with bandaid fixes that ignore the underlying problem. In particular, a cron job that reboots the server when things get overloaded is pretty dangerous, as it could result in a loop of reboot-thrash-reboot-thrash-reboot that makes actually logging in to diagnose the problem very difficult. Also, forcing a reboot like that can result in database corruption, depending on how it is done.
It sounds like a management service, either through your hosting provider or a third party might be a big help to you.
Perfect advice from Panopta & MikeDVB - find the problem and fix it. Does't sound wise to reboot the box when your http daemon is not responding. What does the logs say? What does the system performance utilities (sar, iostat,vmstat...) say? The box should stay up and be accessible all the time (well, as much as possible), otherwise you start losing customers...