Lex... Are you moving to a different USB port? It will typically take a new port, if its plugged in another USB port
If not, try this:
XP Device Manger, by default, doesn't show hidden devices, you have to tell it to. Open a Command Prompt and type:
> SET DEVMGR_SHOW_NONPRESENT_DEVICES=1
Now you should be in Device Manager.
Expand ports and delete/uninstall all non-active ports.
Then uninstall BU-353 device.
Then unplug BU-353.
Reboot without BU-353.
Plug BU-353 in, let it detect, install the driver. Note the COM port.
Reboot and see what the COM port is now. There shouldn't be a new one
If that doesn't change the behavior, theres something weird going on. I've not seen this out of BU-353 or driver... I'd say it leads more to an OS or BIOS thing. Are you using any kind of setup that could keep your puter from "saving", like the Enhanced Write Filter? Anythign unusual about your BIOS config, like disabled ACPI?