Howdy Mr. Phil,
If your Sharps has set triggers, it sounds like you may have a problem with the fly in the tumbler. That's a little flapper that flips forward and guides the sear over the half cock when the trigger is used in the set position. If it is working correctly, it should prevent you from lowering the hammer into half cock from full cock. If your gun does not have set triggers then I'd bet on Thumper's explanation. I'd try to find a gunsmith with some experience with set trigger Sharps to look at things.
Reverend Chase