There seems to be a webserver issue where apache doesn't respond / unreachable on a random basis. I can't see any lead on this but I am seeing a lot of 408 errors in Apache around 2K+ of them almost everyday. Googling around suggest that 408 is an indication of webserver being too busy. The problem is that I can't trap this when the webserver keeps on hanging as the admin will usually just reboot the appliance on the VM.

I'd say you should know how to present your case by now.
- What are the CPU / RAM / storage specs of the VM?
- What does the appliance comprise of? (And I mean full distro and applications versions.)
- When did this situation occur first?
- What happened / changed at the time?
- Is there any SAR / application statistics logging?
- Which system / daemon logs are not clean and where's the full report of errors?
- What dom0 / VM / HW / kernel / SW / (re-)config / service separation / else tuning has been done to remediate the situation already?

as unSpawn stated
this sounds like a basic diagnostic problem

the first two things to look at are

when did this start ?
what changed just BEFORE this started ?

as in IF you installed an update to something ......

if NOTHING was done then
are there hardware related errors in the logs ?