A C172 STUDENT PLT LOSES CTL OF HIS ACFT DURING A XWIND LNDG AND LEAVES THE RWY AT DPA; IL.

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ON MAY/XA/01; I WAS GIVING DUAL INSTRUCTION TO A STUDENT PLT IN THE TFC PATTERN AT DPA. WE MADE 3 TOUCH-AND-GOES -- 1 AT 10 DEGS FLAPS; 1 AT 0 DEGS FLAPS; AND 1 AT 40 DEGS FLAPS. ALL 3 TIMES THE STUDENT DEMONSTRATED COMPETENCY IN SAFELY LNDG THE ACFT. I THEN PROCEEDED TO EXIT THE ACFT TO ALLOW THE STUDENT TO PERFORM HIS SECOND SUPERVISED SOLO. THE WINDS WERE APPROX 230 DEGS AT 13 KTS AND THE RWY WAS RWY 19R; GIVING ABOUT A 01 KT XWIND COMPONENT. THIS STUDENT HAD DEMONSTRATED IN THE PAST REMARKABLE ABILITY TO SAFELY LAND THE ACFT WITHOUT ASSISTANCE IN XWINDS OF UP TO 15 KTS. THE STUDENT TAXIED OUT AND THE TKOF AND PATTERN WENT SMOOTHLY. FROM MY VANTAGE POINT; ABOUT 1/2 MI DIRECTLY ABEAM THE ACCIDENT SITE W; STANDING IN THE DPA FLT CTR; IT APPEARED THE APCH TO LNDG WAS A LITTLE FAST; BUT NOT UNCTLABLE. DETERMINING RWY ALIGNMENT FROM MY VANTAGE POINT WAS POSSIBLE. THE ACFT APPEARED TO BALLOON SLIGHTLY AND THEN SET DOWN ON THE RWY. THE ACFT THEN PROCEEDED TO APPARENTLY VEER OFF THE RWY TO THE L INTO THE GRASS. THE ACFT STRUCK A TXWY IDENT SIGN WHICH APPEARED TO CRIPPLE THE R MAIN LNDG GEAR. THIS WAS ALL I COULD DETERMINE FROM MY VIEWPOINT. IN THE AFTERMATH; AFTER REVIEWING WHAT I SAW; I BELIEVE THE STUDENT ENCOUNTER A GUST OF WIND WHICH CAUSED THE ACFT TO BALLOON AND YAW. THIS WAS NOT CORRECTED FAR ENOUGH BY THE STUDENT AND THE ACFT TOUCHED DOWN ON THE RWY AT AN ANGLE TO THE CTRLINE CAUSING IT TO ALMOST IMMEDIATELY RUN OFF INTO THE GRASS. STRESS LEVELS IN THE COCKPIT AT THE TIME ARE BELIEVED TO BE NORMAL WITH NO OTHER CONTRIBUTING FACTORS TO MY KNOWLEDGE.