It's not clear to me how you have created this PIP - and even less clear on how you are moving this small box. Perhaps a little more description of how will help (me at least) Are you sure you are really trying a PIP - or are you trying to select portions of a clip and move that around the screen?

There are of course numerous ways to handle PIP effects - but typically you would use track motion or pan/crop to do it.

More often than not I choose to use track-motion. If you do that then after you have re-sized/positioned your track to wherever you want it - any cookie cutter or pan.crop mask you have added to the clip will be locked to the motion you apply to the track.