Software

So you're connecting TO this laptop, or from it?

What AP are you using?

What type of WLAN security?

Since the WLAN security settings are stored in the Windows profile, and the profile does not get activated until you login, the security settings for the WLAN must be hosed for that profile.

Is there a personal firewall on the laptop?

Are you using Windows to manage the WLAN adapter or a client utility?

If you turn off WLAN security, letting is connect unencrypted, does it still fail?

Might be something else, but... This may be worth a try.
It may be a case of certificate error/mistrust,etc. Recreate the connetion and when prompted to view the cert place the certificate in the computer's Trusted Root Certification Authority.

Deduct 2 cents...

Purchased an new inexpensive Belkin Connect AP, needed a spare anyway. Set the unit up wide open and getting exact same results.

If the target would have been using Vista or Win7, then I'd ask you to check what "network locations" are attached to ethernet vs the wireless network in question.

But still, try to see if Widnows firewall somehow uses different settings for different SSID or for different types of connections.

Make sure 802.1X authentication is disabled in XP if you're not using it.

I've had this problem ever since getting a new laptop from work. I tried RDP on my home network from an XP machine, or from 2 android devices like i had been able to do previously. The new machine is a windows 7 64 bit laptop. Whenever i would connect via RDP over wireless as soon as I logged in the wireless connection would drop. Confirmed this via pings to and from the remote machine.

I connected the laptop to a wired connection and RDP'd to the IP address i assigned to wired interface and got in without a problem. I then noticed that the wifi had dropped like it had previously. I relaunched the wifi connection from within the RDP session and was prompted for my network's security key. I thought this was strange since my user profile already had that saved. Once I entered the key I was able to connect to wifi. I disconnected the wired ethernet connection, and then successfully connected via RDP to the wireless ip address for the first time! Looks like something must be different with a RDP user profile and one locally logged in. The remote profile didn't have the wifi security key saved and explains why when switching to this user would kill the connection.