Summary

I'm working with some very small objects with hair on a render scale of the minimum .001 global radius.  The render hairs seem to move about the object on different frames.  I don't think it's a Remember issue because I get the same result on a local machine.  I've tried simplifying the object by creating basic hair on a sphere with no modifier and get the same result. 

I'm not 100% sure it's scale related but that's my guess.  I'm attaching a simple max file with an object, a camera, and a light.  If you render the two frames saved in the render setup you should see the same thing.

Max 2014 with Vray 3.05.05