In Office 2007 this is known to happen. Luckly there is a fix in the HowToGeek.com blog:
Hi - I just recently had my outlook asking me for my gmail password on a regular basis making me think I may have visitors - I work for a tech company as well. Here are the 2 IP's that show up besides my own (I use bellsouth dsl)
1 is via IMAP access: 184.108.40.206
and the 2nd is browser based: 220.127.116.11
I never or very rarely use a browser.