Maybe as an instructor on the type you should know the normal idle RPM at best L/D speed, the sound and feel of the Engine at idle in flight etc etc. AND know when it's not right a little earlier BEFORE this happens at low level and catches you out....
The Engine should idle ok during gliding practice ( at what, around 1,000 RPM approx ), if not then the idle speed is adjusted too low. This should have been apparent during the run up checks in the ground when you close the throttle to check the idle speed is around 600 RPM.
Exactly what Sunfish did
What ever happened to running the power up every 1,000' or so to warm the Engine, did you do that?
We're you watching exactly what he was doing or looking out at the view thinking about other things!!
I mean where were you exactly to let this develop?
I'm sorry to be blunt and its your cool head that saved the day but it shouldn't have gotten that far before you noticed and intervened.
Lucky......