Here's a screenshot of a door near world origin:

And this is what doors near world edge look like:

The problem is that a door placed near world origin stays firmly in its place, but doors placed further away from the origin slowly slide down (in direction of negative Y axis, while slider axis is positive Z). The amount they slide down seems to be linearly dependent on the distance from origin. Also, setting the world size smaller stops all doors from sliding down, but that is obviously not a real solution here.
This sounds like some sort of accuracy problem, but shouldn't 32 bit floats be enough for world of this size?
Any help would be greatly appreciated.