Z-Axis doesn't work only during printing Problem:  Z-Axis doesn't work during a print.  It attempts to work, maybe climbs on the Z-Axis, but screws back down.  It whines, too.  But, Z-Axis DOES work while not printing.  It doesn't matter if the bed and nozzle heating or not, if it's not printing, it works as it should.  I don't know what else I can do to troubleshoot this problem.

I have:


Changed the Ramps 1.4 board twice
Swapped drivers around, bought new drivers
Swapped X-Axis and Z-Axis motor connections
Cleaned threaded rod.
Leveled two Z-Axis threaded rod riders to near atomic perfection.
Changed firmware to each of the 3 latest updates
Remounted motor so both face same cardinal direction
Cursed
Changed jumper configurations from 16th microstepper to 8th for more power.  No dice.  Fried two drivers that way.
Dialed and redial and tridialed and quaddialed the driver pots
Recalled the Z-motors work while not printing so it isn't the driver pots
Cursed again
Scoured the web for similar issues
Looked for G-code that might limit Z-Axis elevation
Died a little.  Just a little


Hardware:


RepRap Guru DIY Prusa i3 V2 3D Printer Kit
Ramps 1.4
A4988 Driver
Firmware: 


Marin 1.1.8, 


1.1.7 (screen didn't function), 
1.1.6 (screen didn't function), 

RepRapGuru_Marlin_v4, 
RepRapGuru_Marlin_v2



Additional information:


My power supply is the original 12&nbsp;V 360&nbsp;W supply with the kit.


The 5 amp power in is 12.02&nbsp;V, the 11 amp power port is 11.96&nbsp;V and 12.18&nbsp;V depending on which heater is on. 
The bed measures 11.50&nbsp;V and the hotend is 3.4&nbsp;V

While heating the bed and hotend I am using the LCD screen and rotary encoder to move my axes. It works as expected until printing. I have upgraded to an aluminum 12/24&nbsp;V hotbed from the original PCB.
Currently getting Repetier. Will update.
The z-axis leadscrew is M5-0.8 mm
I would check the gcode you're generating to make sure it's not full of &quot;bad&quot; z-commands.
Further, I'd take any gcode file you have and manually edit it, leaving in all the initializations, heatings, zeroing, etc.,  and then delete everything except some z-motion commands.  Run that as a test case to see what happens.
I  think it's extremely unlikely that the gantry has enough mass to force the z-screws to counter-rotate (lowering the gantry), and you'd see that with power off in any case.
edit
As Greenonline discovered, a bad choice of lead screw might cause the behavior you're seeing.  It would be a bit scary if a stock kit such as the one you bought provided high-pitch Z-screws.  Better check that out!