The clipboard map will reset to it's default position if you had it placed where it's edges are touching the edge of the screen.
If it's not touching the edge, then it will come back up in the position you had it in, at least until you close AH.
I don't move it around myself. I have a button on my stick that brings up the clipboard, and I use this ALOT when cruising around. When in fights I never open it up.