You might have a software conflict of sorts my friend, something that predictable sounds like it's running a cron job (Linux/Unix term basically for a timed process) and is conflicting with the little Wi-Fi adapter.
I suggest temporarily shutting down anything that you don't need running software wise that could be blocking it. One of my first suspects would be to check your firewall settings (XP SP2 has a simple firewall installed) and simply shut down one application at a time to get a simple test. If you actually know what you are doing CTRL-ALT-DEL brings up the task manager in XP, and a quick slide to processes will allow a more detailed "kill and check" style operation to knock off software executing in the background (be careful with this).
Likewise you can always boot into Safe Mode and there should be an option to start windows and check which startup applications and devices you wish to execute. I would help more with this option however it's been awhile since I had to do such and generally when I have to I don't think about it as it's been pure habit for years now.