A BE1900D CAPT RPTED THAT DURING AN APCH TO ACY IN IMC THE CTLR WARNED HIM OF A LOW ALT. THE CAPT WENT AROUND FOR THE ILS.

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IT WAS THE 4TH LEG OF AN 8 LEG; 14 HR SHIFT AND THE 3RD CONSECUTIVE DAY OF 5 LEG; 14 HR SHIFTS. THIS EVENT OCCURRED ON THE 12TH INST APCH IN 2 DAYS IN LOW IFR WX WITH MODERATE TURB ON ALL APCHS. WE WERE BOTH TIRED WITH THE USUAL AFTER LUNCH COBWEBS; BUT HAD 4 MORE LEGS TO GO BEFORE WE WOULD GET HOME. AFTER BRIEFING THE VOR 4 APCH WE RAN ALL CHKLISTS AND HAD THE ACFT CONFIGURED PRIOR TO THE FAF. I HAD MENTIONED I WAS TIRED TO THE FO A WHILE BACK; BUT THIS IS PRETTY MUCH ROUTINE ON THIS SHIFT. WE CROSSED THE FAF AND I STARTED MY DSCNT TO THE MDA OF 480 FT. I THINK THE FO WAS A LITTLE BEHIND AT THIS POINT BECAUSE I DO NOT REMEMBER HIM KEEPING UP WITH THE STANDARD CALLS; BUT THIS COULD ALSO HAVE BEEN MY NOT HEARING THEM. THE RADAR ALTIMETER CALLED 'MINIMUMS' AT 410 FT AGL AND I REMEMBER BEING SURPRISED THAT WE WERE THERE ALREADY. ALMOST SIMULTANEOUSLY THE TWR GAVE US 'LOW ALT' WARNING AND INSTRUCTED US TO CLB BACK TO MDA. I HAD ALREADY LEVELED OFF AND WAS INDICATING 480 FT ON MY ALTIMETER. WE WERE NOT YET AT THE MISSED APCH POINT; VISIBILITY WAS POOR IN LIGHT RAIN AND I REMEMBER FEELING VERY CONFUSED BY EVERYTHING THAT HAD JUST HAPPENED IN THE LAST 3 SECONDS. AT THAT POINT I DECIDED TO GO MISSED APCH SO WE COULD GET AWAY FROM THE GND AND REGROUP. AFTER THIS; I ELECTED TO DO THE ILS TO RWY 13. THERE WERE NO FURTHER PROBS. CONTRIBUTING FACTORS: 1) FATIGUE. 2) RELATIVELY INEXPERIENCED CREW.