It really sounds like the acceleration/feedrate is the problem causing the steppers to lose steps.
The clue: "is making a distinctly audible humming noise while stalled."
This can be caused many things. Here are some.
1. While moving above a critical speed the PC interrupts the smooth flow of pulses (pauses for some milliseconds).
Above a critical speed the stepper cannot instantaneously change speed. Inertia wins.
IDE drives (CDROM or HD) can steal cpu cycles with DMA interrupts.
If your BIOS allows disabling DMA access to the hard disk, this often will fix it. A hard disk in poor condition will can make the PC go off in the 'weeds' and Windows doesn't care. You just drop CPU cycles for the end user. Tuff!
SCSI drives do not create this problem.
2. Stiffness or restriction in the movement. This would not appear to be the case unless the X axis is also sticky.
3. Motor tuning is not optimal..
4. The power supply voltage to the drivers is lower than what it was for the original setup for motor tuning, or your stepper motors characteristics are different.
Initial tests to resolve this problem: Item 3.
Reduce the acceleration setting to half of what it is, and reduce the max speed rate to half or even much less.
Keep halving the rate(s) until the problem is not there.
Now keep increasing the max speed until you get the fault.
Reduce the setting that works reliably by maybe 20%.
Do the same now for the acceleration until it faults, then reduce by maybe 30%.
Do this for each axis.
Do the tests under program control as the rapid feeds are not the same process as rapid feed jogging.
For test purposes, do one axis at a time just using rapid to move backward and forward between 2 points, just marked with a pencil on the slides.
You can use the Mach3 feed control slider to increase or decrease to save a lot of changing of the tuning.
When you find the sweet spot, multiply the tuning value by the slider setting, then go back to 100% to fine tune further.
While you use IDE drives, there is always a possibility of interrupted pulse train(s) to the driver(s) above a critical speed.
On my machine, for critical work I halve the max speed, as insurance.
It clunks (which makes your heart miss a beat) but NEVER looses steps, after 1500 hours of the odd clunks, machining expensive material. It a 2GHz CPU, with IDE drive, and DMA can't be disabled. Thanks IBM !!
Super X3. 3600rpm. Sheridan 6"x24" Lathe + more. Three ways to fix things: The right way, the other way, and maybe your way, which is possibly a faster wrong way.