Maybe I should mention that I've seen this exact problem on our Dell laptops as well!
We used some Intel wireless client software that came with the driver, but it kept re-authenticating. I even talked to HP about it.
We ended up using the WinXP-build-in WPA-client and everything started to work just fine.
But this might indicate that the AP itself has some issues with certain wireless clients! Are there any HP tech guys reading these forums? If there is, maybe you could look a little into this, and find out whether this is a known issue?
Rgds,
Rasmus