Hi Cameronian!
Had the same thing happen to me a couple of years ago - blerry irritating I agree! I rather think it started happening after the installation of SP2 or SP3. Problem is -- I can't remember just how I sorted out the problem!
Reloading Outlook Express might present a few problems - like where would you get it in the first place? As far as I know - it was an integral part of Win XP and was automatically installed when you (or the original OEM) installed the operating system. Secondly, (again
afaik) when Outlook Express (and Outlook itself too) are installed, they assign a gobbledegook "User ID String" when installed - not normally seen by the user - and you effectively would be installing a second Outlook Express account.
But fear not! You are not alone!

Try Googling:
stop microsoft outlook express asking to compress files - this will bring up about 686 000 hits - and I'm sure that at least one of the responses might be of some help!
Hope that helps!
PS Just checking one of my XP machines - It still has a folder for
Outlook Express in the
Program Files folder - so it doesn't actually go away too easily!