Did you check the nose of the sear? I have seen some that the nose broke off of and they were cleanly broken so that they would catch the full cock notch, but were too thick to engage the half cock notch.
Also, check that all the screws are tight, but not too tight. If the bridle or sear has too much play the sear might not engage properly, although that usually affects the full cock notch before it's noticed in the half cock notch. If the screws are too tight anything in the lock that is supposed to move might bind.
Go to the Tutorials section and read Jim Chambers post on Lock Tuning.