...what I'm asking is there normally some point toward the extreme limits where the polar mount just won't stay on the arc, and hence can't see the satellite?
There is no point at which it leaves the arc IF the azimuth and elevation have been set accurately.
Do you have a squacker or any other kind of signal meter? If so, then disconnect the jack arm and peak it at the lowest satellite on the horizon you can see to the west, and then swing it all the way over and it should be a bullseye to the lowest in the east (which may be difficult to do if the only ones at either extreme are circular only but you don't have a circular feed) If you can't peak both from the same mount settings then either your elevation is off or your declination is off..
The maximum tracking error anywhere along the arc using a modified polar mount should only be about a tenth of a degree.
Have you tried to conceptualize how polar tracking works? The satellites are in a circle. If you put a dish on a vertical mast on the north pole with no declination angle, it would sweep out a plane parallel to the equatorial plane and hit nothing, but if you tilt the mast forward, the intersection of the two planes would be a straight line.
So instead, we introduce a declination angle that results in the generation of a cone that exactly intersects the Clark Belt. But it only tracks perfectly if it is on the north or south pole.
In real life, we are tracking from points that are closer to the belt section we are trying to track than is the north pole, so if we set up our mast at exactly our elevation angle and set a declination angle that intersects with the southernmost satellite, then that mount would track to the inside of, or underside of, the arc, because the intersection circle would be smaller than the Clarke belt, but if we instead set a declination angle equal to the real declination angle to the western-most visible satellite, then we would track above the Clarke belt, so the best compromise is to set the dish at the declination angle that corresponds to the lowest satellite on the horizon but when it gets to the top of the arc, fudge the elevation angle to get a bullseye there.
You need to precisely affirm and set your elevation angle and you need to use the so-called "modified polar mount" declination angle rather than the southern intercept declination angle.
I maintain a horizon to horizon mount for a government contractor that designs specialty receivers, and we have no trouble maintaining virtual bulls-eye aim from horizon to horizon using a cheap junk Radio Shack modified polar mount.
