A B737 PILOT REPORTS MISSING A CROSSING ALT RESTRICTION CAUSED BY THE DISTRACTION OF THE MCP ALT SET RESETTING TO FL500 SEVERAL TIMES DURING DSCNT.

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APPROX 40 MI S OF ZZZ WE WERE GIVEN A CLRNC TO CROSS ZZZ AT FL280; THEN DSND PLT'S DISCRETION TO FL240. PUT XING RESTR IN FMC AND SET FL240 IN MCP WINDOW. JUST BEFORE TOP OF DSCNT WE GOT AN ALT ALERT HORN AND WE NOTICED THE MCP ALT WAS SHOWING FL500. I RESET THE MCP ALT TO FL240 AND ELECTED TO START DOWN EARLY USING VERT SPD TO MAKE XING RESTR. AT APPROX FL320 THE ALT ALERT HORN WENT OFF AGAIN AND THE MCP WINDOW RESET TO FL500 AGAIN. WE AGAIN RESET FL240 IN MCP WINDOW. THIS SEQUENCE OF EVENTS HAPPENED AGAIN AT APPROX FL310 AND AGAIN WE RESET THE MCP ALT TO FL240. EACH TIME THIS HAPPENED I VERIFIED MCP ALTS WITH PNF. ANYWAY; I GOT DISTR ENOUGH THAT WE CROSSED ZZZ AT FL284 INSTEAD OF ASSIGNED ALT FL280. DISTRS WERE: 1) WORKING WITH ZZZ1 MAINT ON ANOTHER PROB VIA ACARS. 2) 3 TIMES THE ALT ALERTER WENT OFF AND THE MCP ALT RESET TO FL500. THIS HAPPENED IN A SHORT TIME SPAN. 3) ATC ASKED US TO SLOW TO 250 KTS ABOUT 2 MI BEFORE ZZZ WHICH I DID AFTER I GOT BELOW FL280. BOTTOM-LINE: I GOT DISTR ENOUGH WITH THE MCP ALT ALERT HORN AND MCP ALT WINDOW RESETTING TO FL500 3 TIMES IN A SHORT TIME FRAME AND CLOSE TO ZZZ. I HAD GOOD INTENTIONS WHEN I STARTED DOWN EARLIER VIA VERT SPD RATHER THAN WAITING FOR VNAV TO START THE DSCNT; BUT I DIDN'T HAVE ENOUGH VERT SPD SELECTED FOR WHAT WAS NEEDED TO MAKE THE XING RESTR. MAYBE I SHOULD HAVE LET VNAV DO THE FLYING; OR TOTALLY DISREGARD THE PROB AND WORK ON THE RESTR FIRST; OR MAYBE I SHOULD HAVE TOLD ATC THAT WE COULD NOT MAKE THE RESTR THAT WE WERE WORKING ON A PROB.