Steve,
Who made the lock and lock parts? Did someone work on the lock to lighten the trigger pull?
I am not going to suggest anything different than what others recommended. I just thought you may like a little more complete explanation of what we mean.
When you view the full cock notch from the side of the lock with the internal parts facing you, the notch should be perpendicular to the center of the tumbler or even angled back slightly towards the rear of the lock to the right. A rearward angle should only be 2-3 degrees at most, though. (Military musket locks had/have notches that are angled towards the rear even more than that, but that is why their trigger pulls are so heavy.)
I agree with others the full cock notch is either rounded off or someone filed/changed the angle so it is angling forward from perpendicular to the center of the tumbler. Some people file that notch angling forward to lighten the trigger pull, but that is the wrong way to do it as the sear tip will slip off the notch as it seems to be doing in your case.
If the full cock notch is rounded off or angled to the front too much, that notch will have to be filed/stoned to the proper angle and then the tumbler re-hardened and annealed. If the notch is not re-hardened and annealed after this work, it may only last for between 1 and 25 times of cocking before the notch is rounded off again and won’t hold at full cock. If the sear is not worn much or not chipped, then it may not need fixing or maybe only a little stoning. If it is worn much or chipped, it will also need reshaping and perhaps re-hardened and annealed as well.
Some times when a full cock notch is rounded off/chipped too much, there is not enough metal left to fix the angle of the notch or other problems can arise. Then the notch must be welded up, reshaped, re-hardened and annealed.
The easiest/fastest way to get the lock fixed is to order a replacement sear and tumbler as others have recommended. The trigger pull is going to be different and most likely heavier, though, with the new parts installed. That is normal until/unless someone does a proper lock adjustment for a good trigger pull.
Gus