We've heard some reports of an issue where, in some cases, Axton's action skill is activated by the player, but the turret does not deploy. When this happens, the duration bar appears on the screen, and winds down to empty. Once the cooldown recharges, the ability should be usable again.
This issue may be caused by the turret spawning under the terrain. In this case, you may be able to cancel the turret to speed up the cooldown.