B737-200 HAD EXPERIENCED EXTENDED DELAYS DUE TO MAINT PROB AND EVENTUAL ACFT CHANGE. FLEW ZZZ1-ZZZ2-ZZZ1-ZZZ3-ZZZ AND SCHEDULED TO CONTINUE TO ELP. CAPT ELECTED TO CANCEL ZZZ-ZZZ3 SEGMENT ACCOUNT FATIGUE.

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CHKED IN AT XA10 ZZZ1 TIME. FLEW ONE LEG TO ZZZ2. MAJOR MECHANICAL INVOLVING #2 ENG AND #L-2 DOOR HANDLE VIBRATING UNLOCKED INFLT. 3 1/2 HR DELAY. MAINT RAN ENG AND SAID IT WAS OK FOR CONTINUED FLT PER MAINT MANUAL. WE TOOK OFF BACK TO ZZZ1. SAME ENG PROB AND ANOTHER DOOR PROB. ACFT REMOVED FROM SVC IN ZZZ1. I WENT UPSTAIRS TO MAINT CTL. THEY KNEW ALL ALONG THE ENG WASN'T CORRECT AND JUST HAD MAINT SIGN IT OFF TO GET IT TO ZZZ1. WE GOT ANOTHER ACFT AND WENT TO ZZZ3. CALLED SCHEDULING AND ASKED IF WE WERE GOING TO HOTEL IN ZZZ3; OR WERE WE TO GO TO ZZZ THEN BACK TO ZZZ3. THEY SAID TO CONTINUE. I TOLD THEM BARRING A MIRACLE WE WOULD HAVE TO STOP IN ZZZ. MY FO FELL ASLEEP ON DSCNT INTO ZZZ FOR A FEW SECONDS. I STOPPED THE OP IN ZZZ; WAS TOLD TO RPT TO ZZZ OPS AND AWAIT PHONE CALL FROM CHIEF PLT. I DID. TOLD HIM THE STORY. HE SAID GOOD JUDGEMENT. MONDAY AFTERNOON RECEIVED PHONE CALL WHILE I WAS ON LAYOVER IN ZZZ2 FROM B737 FLEET MGR STATING THE SENIOR VP OF OPS WANTED AN INVESTIGATION AS TO WHY I REFUSED TRIP THAT WAS ONLY 12 HRS 45 MIN DUTY DAY WITH A PLANNED ARR INTO ZZZ3 AT XA30. POSSIBLE SEVERE DISCIPLINARY ACTION TO FOLLOW. SINCE MY FO AND I ARE COMMUTERS; THEY ARE TRYING TO SAY WE DIDN'T SHOW UP RESTED WHICH IS UNTRUE. THEY DO NOT UNDERSTAND THE PROBS OF CRAPPY MAINT AND THE ASSOCIATED FATIGUE OF DEALING WITH POOR MAINT OR NO MAINT.