Richard - I run mine with antifreeze, as do many others, not least for the antimicrobial nature of the stuff (stops algae grow if exposed to light). Yeah, if the motor is not under excessive load you can run them without coolant. It's heat, not absence of coolant that will kill the motor - until the motor gets hot you're not risking an awful lot.

You have limited reasons to lose Z positioning -

(from the sharp end, backwards...)

Collet not tighten (bit rides up into collet, been there, done that - marker pen, witness mark on the shank of the bit.
Spindle clamp not tight (spindle rides up into clamp - unlikely!, marker pen, witness marks)
Z-axis ball-nut mount - unlikely
Z-axis ball-screw mount - unlikely
Z-axis ball-screw to motor coupler - check the grub screws are tight. Use marker pen to add witness marks to spindle/coupler.
Z-axis stepper stalling - check stepper driver current settings. Harder to prove without risking damage.
Z-axis stepper signalling - dodgy wiring. Check by calibrating Z0, then run a few hundreds/thoasands G0Z20/G0Z0 cycles.
Z-axis stepper signalling - short pulse-widths - unlikely if your Mach3 kernel is lower that 100kHz.