Sounds like something may be "cleaning" the licence file away, or maybe preventing Opus from saving it to disk so that it is only in memory until a restart.
Zone Alarm, under certain configurations, is known to have caused that problem in the past. There's a FAQ about it which may help, if you use ZA: Registration certificate suddenly expires or does not stick.
If you're not using ZA, or the FAQ doesn't help, it could be a file-permissions problem. I don't have an XP machine to hand to check on but under Vista I believe this is the path which Opus will try to write to to save the licence details:
C:\ProgramData\GPSoftware\Directory Opus\dopus.cert
It might be under Program Files (i.e. the main Opus directory) on XP but I'm not 100% sure. It should be the only copy of dopus.cert on the C:\ drive so a search should confirm whether it was saved correctly or not.
If Opus cannot create the dopus.cert file in that directory (or the XP equivalent) then that may be causing the problem.
I guess it's also possible that the file is saved in a way which doesn't let Opus read it, if the permissions are in an unusual way. If you find dopus.cert, try opening the viewer pane to confirm that you can see a hex view of the file. (Don't post a screenshot of it, though. It may contain licence details.)