Composite of tracked image-as-plane: reflection of emission not showing

Can’t understand what’s going wrong:
I’ve got a image-as-plane movie composited into a scene where I have a blank laptop screen; the screen reflects off of a “floor” plane that is acting as a transparent reflector (cycles). The reflection appears in the rendered view, and sometimes - but not always! - works when composited. Not as a frame-by-frame, just sometimes it’s there, sometimes it isn’t.

I thought at first it was due to the movie being a .mp4, so I imported it as still frames. Viola, it worked, I could get a reflection. Then, it disappeared again. Came back. Etc. I’d finally gotten it to where I think it was working properly, then finally got a mask (to occlude an object in the foreground of the composited movie clip) working, and then GONE! I wasn’t doing anything to the reflection plane or it’s render layers or nodes at the time.

I’ve played with render layers, blur (to nothing), looked at the outliner to make sure it’s visible to renders, everything I could think of. There’s nothing in the way of it (checked the mask in the viewer). I’m flummoxed.

Could it be a texture memory issue if using a graphics card to render? Does the image disappear only from the reflection or from both sources?