The wikis state something like this : "Sometimes if the player takes the perk Quick shot, the arrow will not travel very far despite the animation showing the arrow beeing completely pulled back. Loading a previous save will fix this."
But I have kept playing and saving the game for quite alot of time after getting the quick shot perk and getting this bug, so I no longer have a save from before that. Loading any other save of that character after quick shot, making a new one and loading that does NOT work. Bug still exists.
Some have suggested trying different bows, re equipping the items, etc. but none of it works.
After some time googling I have not been able to come up with a fix for this and it really ruins archery in this game for me.