The condition you describe is usually caused by excessive clearance between the top of the disconnector and its port at the top of the frame. When you pull the trigger through the second stage, the sear exerts rearward and because of the angles of the contact surfaces, upward force on the disconnector itself.
In battery, the bottom of the slide limits the disconnector's upward movement and the sear is tripped. When there is excessive clearance at the top of the disconnector, its upward extension grates against the slide until it bears against one side of the port. This is why you don't feel the 'click' with the slide off.
The condition is caused by a worn or out of spec disconnector, a worn or out of spec frame port, or both.
The correction is to first replace the disconnector with a new, full dimension factory part. FWIW I've had good luck with Wilson 'Factory Plus' parts. You can count on those to be in-spec with USGI blueprints. Cylinder & Slide and several other reputable outfits offer 'match' disconnectors which are already polished in the right places to facilitate a smooth pull.
If your frame port is worn or oversize, it's more complicated. If you examine old AMTU built target 1911s you will often find one or two punch marks near the disconnector port in the frame, where they have closed it up and reamed it to minimum dimensions to accomplish a crisp second stage of the pull.
Hopefully a new disconnector will solve your problem.
