Do you shoot at things from afar or from close range? I think the farther the target is from you, the more skill increase you get.
Try shooting some 10-20 shot from at least 7-8 tiles away (if you have the latest experimentals and the options to wait a bit to increase confidence and steadiness - do so) and tell us if it goes up or not.
Also, try to use the best bow/arrows you can, with the least dispersion, try to mod your bow to the max too, if not already.