The fan has a 'anti-burnout' function. If it experiences too much resistance, it keeps trying for about 3 seconds. After that it quits, until you either restart the vehicle, or unplug and plug it back in.
See my ancient post for reference:
http://www.thenissanpath.com/viewtopic.php?t=1654
Its possible its getting old and the brushes are worn, which could cause the resistance in your case. I would suggest either getting it rebuilt or finding another one if that is the case, as it is just a matter of time. Just went through that in my 2000 Grand Prix, it totally quit on me about a week after the first time it didn't fire up properly. Got a wrecker part for $20.
Or did you find any dirt or leaves in it that could have caused it to kick in the 'anti-burnout' function?