"Both the rear lock bolt screw and the forward bridel screw may, stick out from being flush with the lock plate and bind against the inside of the hammer. Either of these will slow the speed of the hammer fall due to friction or binding.
Because both of these screws are hiden by the hammer, they are often over looked as a potential problem.
Dismantle the lock and check that the sear screw and the bridle screw had not been swapped. Putting them into their correct configuration should solve the problem instantly and permanently.
Check to see if the trigger is in the right place, it might not be pushing the sear far enough out of the way, check too to see if it is worn on the top. Make sure the sear is moving freely and the spring is in the correct place. If everything is assembled correctly then the whole thing is simple enough it usually works which goes back to if you are pulling the trigger back far enough or just tapping it and not holding it back. The amount of travel to release from full cock is not as much as it needs to clear half cock, you have to find why it isn't going the distance be it something you are doing, a mechanical problem, something binding such as a bit of wood in the way (look for recent scrapes in the lock inlet, nothing should be rubbing) or a screw too tight or too loose (the tang screw could be too long or not tight enough and has the trigger too far away to engage correctly). Hard to tell you without having the musket."