I always undock my browser since I need it to have a white instead of transparent background for the sake of my sanity. It jumps to my other monitor all the time - sometimes after updating a feature in the timeline, sometimes when switching between open files, very often when opening a drawing, etc. I just started using the latest update so I don't know if it's any better or worse, but so far it is staying in place for me when I open and close the data panel.
