Do I need to change the password for a scheduled task on Windows XP if I change it?

Yes, after you change your user password it will break the scheduled task. You must either:

1. Run it as Local System, Local Service, or Network Service
2. Use a special user created who's password does not change.

For option 2, if you create a local user on the computer (not a domain user) it will not be required to change it's password like the domain user, however that user will not be able to access network resources. You may want to try running your task as NetworkService if you do need to access network resources, but you may need the help of IT so your computer has rights to access whatever network resource you are trying to use.