Thank you for your timely and sage advice.
I, by good fortune, have a highly accurate method of homing the machine. Built into the mill is a precisely accurate mechanical position readout, allowing me to position the bed to exactly the same position repeatedly. It is foolproof.
Therein lies my problem. When I exit Mach3 I make sure the bed is positioned precisely where I want it. When I start Mach3 the bed moves slightly. So I reposition the bed to where I want it before pressing ResAll. Pressing ResAll jogs the bed to precisely where it moved to when Mach3 started and sets Current Position, Machine Coord, and Work Offset to zero at that location, not at the location I moved it to. When I return the bed to the location it was in when I pressed ResAll, the Machine Coord and/or Work Offset is changed by the amount the bed originally moved.
I have a feeling I am going to have to make a video to show what is going on.