AN ACR INSTRUCTOR PLT RPTS THAT TWICE HIS STUDENT DSNDED; WHILE THE INSTRUCTOR WAS DISTRACTED; TO THE POINT THAT THE GPWS ALERTED. EACH TIME THE INSTRUCTOR TOOK OVER AND PERFORMED AN ESCAPE MANEUVER.

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LATE NIGHT TRAINING FLT; PART FAR 91 REG. AFTER DOING A SPECIAL DEP FROM JUNEAU WE WERE GOING OUT AND MAKE A 180 DEG TURN AND LAND. THE ACFT IS EQUIPPED WITH ENHANCED GND PROX SYS AND IT WAS ON AND SHOWED SOME TERRAIN IN THE GREEN BAND AT 12 O'CLOCK POS. I VECTORED THE STUDENT ON A MODIFIED PROC TURN. I PUT MY HEAD DOWN TO GET THE VREF NUMBERS AND HEARD THE GND PROX WARNING; 'CAUTION TERRAIN.' I TOOK OVER THE CTLS AND PERFORMED OUR ESCAPE MANEUVER AND GAVE THE JET BACK TO THE STUDENT. THE STUDENT ALLOWED THE JET TO DSND AGAIN WHILE MY HEAD WAS DOWN. AGAIN THE GND PROX WENT OFF 'TERRAIN.' ONCE I DID OUR ESCAPE MANEUVER AGAIN AND FLEW THE AIRPLANE TO THE FINAL APCH COURSE AND LET THE STUDENT LAND. THERE WERE ONLY 3 OF US ON BOARD. ANOTHER STUDENT WAS IN THE JUMP SEAT. I ASKED THEM IF THEY SAW THE TERRAIN ON THE ENHANCED DISPLAY AND THEY SAID YES. THEY THOUGHT I WOULD TELL THEM WHEN TO TURN. I TOLD THEM TO FLY THE JET FIRST REGARDLESS OF WHO IS IN THE L SEAT (I'M A CHK AIRMAN). I SHOULD NOT HAVE LOOKED AWAY WHILE IN THAT PHASE OF FLT WITH NEW STUDENTS UNFAMILIAR WITH THE AREA.