I had a King KI209 (the VOR/LOC/GS head with built in converter) fail in flight with no flag. We were IMC on vectors to a short gate ILS at an airport with no DME. The student was late starting the descent so I was not surprised to see the GS full down but it remained full down when we intercepted the loc. I finally realised what was going on when we were only 100 ft above the FAF GS check altitude still with a hefty descent rate and the needle had not budged. I called missed approach and we went home flying the lOC/DME to minimums to get back in. The instrument never showed a flag and intially passed its bench test. After cooking for awhile it finally replicated the fault. Bottom line any piece of electronic magic can fail, sometimes in subtle ways, so keep your situational awareness and when that little voice in your head is saying "hey that ain't right"....listen !