Last night when I shut my machine (a BP clone knee mill) down I moved the X & Y to 0,0 and hit the Estop. I noticed this morning when I was ready to fire it up that Y was at 0.001 and X was at 0.0001. So something moved and there was a pretty large temperature change over night. No problem on that machine because the scales are on the table, not reading lead screw position. A temperature change would be my guess.
On my son's Haas TM-2P, the X seems to lose the G54 position on power down, the Y seems to be OK. Sitting idle for a few hours or even overnight seems to have no effect on the position as long as the main power is left on and the computer hot, with the machine just Estopped.