WM Recorder in the PRO mode is IMHO the best way to record password-protected streams.
And in this mode WMRecorder records what your WMP plays, so you can't (you shouldn't ) close the WMP while recording.

As for NetTransport it was free, but it's shareware now (free to try for 90 days).

Try to enter username and password in the properties dialog of NetTransport. It is usually better than just adding them to a URL, 'coz NetTransport supports several types of authentication.

p.s. These two programs are the only ones I can suggest for password-protected-streams.
Try to add username and password in the Properties dialog. It could help. While WM Recorder is highly recommended, NetTransport is just recommended