Are there any Windows video players that don't stutter when looping?
As mentioned, if all players stutter for you then the issue probably isn't the players.
Check the clip to see if the last GOP is 'ragged'. Looping works best when the clip ends cleanly, that is, exactly at the end of a GOP.
ETA:
Many modern codecs are very good at minimizing file size and bandwidth, but one of the things they assume is that the material will be played straight ahead. A clip as short as yours may in fact have only one I-frame (complete frame), at the beginning.
Try encoding in an all-I-frame codec like MJPEG and see if you have better luck.