I don't have any idea why Apache is shutting down. The first thing I would look at in this situation is the Apache logs. Then maybe I would look at other logs, like the php log, etc.
Last week I had to check an installation of Moodle with XAMPP ... it had the same problem. I found out that there was a web server running with NERO software instructions ... bad thing ... you install a cd burning software and in the background it also installs a web server.
Assuming you're using Windows, make sure Micro$oft haven't sneaked IIS in while you weren't looking.
i am using Xampp for "My Moodle on a USB Stick" on Windows machines
and have had the same (similar) problem : but only when i change PC
it was the address (H: and not E: ) which had changed
(If you prefer to ring them the number is 08700 668617.)
For about the price you'd pay for the stick in PC World.
This version uses The Uniform Server rather than WOS (which in my view is more robust) with some tweeks, and has Moodle 1.8+ on it. There is also two hard drive versions, one of which works on a network.
You might still have to sort out your machine if Apache is running elsewhere on it. Usually, it's IIS running on the machine. There's some support with the stick to get you through these common problems.
Is there a particular reason you want it on a stick rather than install on the machine? Indeed, have you installed it on the machine and that's why Apache might be running elsewhere?