I found a Youtube video about this phemomenon:
In the comments the poster of the video says he
thinks it might have started after his bow was shouted out of his hands by a Draugr.
Another said it happened after he got his bow back either during or after Diplomatic Immunity
One comment claims it started for that person after he had the bow equipped and went into Beast form although that player likely broke his game in lord knows how many ways as he said he had 9999 Archery skill.
The most comprehensive solution suggested was to drop the bow, equip a different set of arrows and pick up the bow and re-equip it.