PA28 EXPERIENCED FUEL STARVATION ON FINAL APCH. THE OTHER FUEL TANK WAS SELECTED AND THE ENG RECOVERED.

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TRAINING FLT WITH PRIMARY STUDENT (PRE-SOLO APPROX 25 HRS). DID AIRWORK IN LCL PRACTICE AREA THEN PROCEEDED TO NEARBY ARPT FOR SOME LNDGS; WINDS WERE 220 DEGS AT 15 KTS GUSTING 25 KTS. LEFT AFTER 3 TKOFS AND LNDGS FOR RETURN TO ZZZ. CALLED ABOUT 8 MI OUT AND WAS TOLD TO RPT FINAL FOR RWY 16 (WINDS 21 DEGS AT 15 KTS GUSTING 25 KTS). ABOUT 2 MI OUT THE ENG STARTED TO CUT IN AND OUT. HAD STUDENT IN L SEAT SWITCH TANKS; CALL ATC AND SAID THAT WE HAD A PROB WHILE COMPLETING THE REST OF THE EMER RESTART. ENG SMOOTHED OUT ABOUT 5-10 SECONDS AFTER SWITCHING TANKS AND THE LNDG WAS UNEVENTFUL. ATC ASK WHAT THE PROB WAS AND I TOLD THEM THAT I THOUGHT WE HAD RUN 1 TANK DRY (WE FLEW 1.2 HRS). HOW THE PROB AROSE: ALL OUR ACFT ARE TOPPED OFF BY LINE SVC EVERY NIGHT. THIS ACFT HAD BEEN USED LATE AND DID NOT GET REFUELED. I HAVE A HABIT OF NOT SWITCHING TANKS AFTER A LCL FLT IF THEY WERE FULL WHEN WE DEPARTED. I LET MY STUDENT DO THE PREFLT INSPECTION UNATTENDED AND DID NOT VISUALLY CHK THE FUEL LEVEL MYSELF. WHEN I ASKED HIM HOW MUCH FUEL WE HAD ON BOARD HE SAID WE HAD HALF TANKS IN BOTH WINGS. I DID CHK AFTER WE LANDED AND THE L TANK HAD ABOUT 12-14 GALS LEFT. IT IS MY RESPONSIBILITY TO ASSURE THE FUEL LEVEL VISUALLY AND I DO MOST OF THE TIME. CONTRIBUTING FACTORS: 1) THIS ACFT HAD HAD A PROB THE PREVIOUS DAY. IT HAD STALLED ON A TXWY AFTER LNDG AND I WAS TOLD TO WATCH FOR A PROB. 2) WE WERE IN MODERATE TURB. CORRECTIVE ACTIONS: 1) USE THE CHKLIST; USE THE CHKLIST; USE THE CHKLIST! DO THE ITEMS COVERED EACH AND EVERY TIME FOR EACH AND EVERY PHASE OF FLT. 2) VISUALLY CHK FUEL LEVELS. 3) STAY WITH THE STUDENT DURING PREFLT INSPECTION. 4) PRACTICE WHAT I PREACH.