Placed .psd or.ai files become blurry upon playback

When I place a .psd file (in this case a cutout of myself with type next to my head) it looks high rez until the video actually starts playing, then it becomes low rez? How to avoid this and/or keep placed .psd or .ai files high rez? I've attached a screenshot that shows the file when placed and then how it looks as soon as I hit the play button.

Thanks!

Dave