B737 CREW LNDG SAV IS INFORMED OF A MISSED HEADING ASSIGNMENT BY ATC.

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ON DSCNT INTO SAV; APCH CTLR ADVISED US WE HAD MISSED A TURN ISSUED BY THE PREVIOUS CTLR TO A 180 DEGS (WHICH WOULD HAVE GIVEN US A DOWNWIND TO ILS RWY 36). WE COMPLIED WITH THE HDG INSTRUCTION AT THAT TIME AND THE REST OF THE APCH AND LNDG WAS UNEVENTFUL. NEITHER THE FO OR MYSELF COULD EVER REMEMBER THE HDG BEING ISSUED. WE PRESUMED IT WAS ISSUED DURING EARLIER PART OF THE DSCNT. WE WERE VERY BUSY BECAUSE ARPT WX DROPPED FROM 1200 FT OVCST/8 MI TO 800 FT OVCST/2 1/2 MI IN A 27 MIN FLT. THIS PROMPTED A CHANGE IN APCH AND RWY -- A RWY THAT WAS SHORTER; UNGROOVED AND WET. WE WERE VERY BUSY REBRIEFING THE APCH AND DISCUSSING THE PROPER FLAPS; AUTOBRAKES; ETC. WE CAN ONLY SURMISE THE HDG WAS PART OF AN INTERMEDIATE DSCNT CLRNC GIVEN DURING OUR REVISED APCH BRIEF. WE FOUND IT ODD THAT THE ISSUING CTLR DID NOT 'CORRECT' US A FEW MOMENT AFTER GIVING US THE HDG. INSTEAD WE GET A FREQ CHANGE TO A NEW CTLR WHO THEN WAITED A FEW MOMENTS BEFORE ADVISING US WE HAD NOT TURNED AS INSTRUCTED TO DO EARLIER.