I personally like how Shadow of the Demon Lord did this:
Once you empty your quiver of five arrows, you still have arrows until you crit fail to shoot. Then, you must refill your quiver from your backpack during combat or have no ammunition to shoot with until you get more. In that system, crit failing is rolling a dice total of 0 or less, which is only possible with really low rolls on the d20 and getting hit with a really high d6 penalty from banes.