FLC OF A B737-400 FAILED TO CROSS ALT FIX AT ASSIGNED ALT RESULTING IN ATC INTERVENTION TO REMIND RPTR THAT THE FIX HAD BEEN OVERSHOT. ATC AMENDED CLRNC FOR OTHER ALT XING FIXES.

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CRUISING AT FL240; ATC ISSUED 'CROSS 15 MI S OF DNY AT FL190.' I READ BACK CLRNC. FO (PF) ENTERED XING RESTR IN FMC. A FEW MINS AFTER THAT; FO MADE PA TO PAX. AS HE STARTED PA I WENT TO DSCNT PAGE ON FMC. I NOTICED WE STILL HAD 24 MI UNTIL TOP OF DSCNT. ALL I LOOKED AT WAS JUST THAT; AND NOT TOP OF DSCNT FOR 15 MI S OF DNY. TURNS OUT 24000 FT UNTIL TOP OF DSCNT WAS FOR NEXT WAYPOINT DOWN THE ROAD. JUST ABOUT THE TIME WE REALIZED THE PROB; ATC INQUIRED WHEN WE WOULD BEGIN OUR DSCNT. I REPLIED 'NOT FOR A LITTLE WHILE YET.' I WAS STILL THINKING WE HAD A FEW MORE MI YET. HOWEVER; AN INQUIRY FROM ATC ABOUT YOUR ALT USUALLY SENDS A JOLT OF ADRENALINE AND WE BOTH CHKED OUR DISTANCE FROM DNY. TO OUR SHOCK; WE WERE ABOUT 20 MI S; ALREADY PAST THE XING RESTR; AND STILL AT FL240. ATC THEN ISSUED THE FOLLOWING; 'JUST CROSS LHY AT 12000 FT.' NOTHING FURTHER WAS SAID ABOUT IT BTWN ATC AND US. AFTER REFLECTING ON THE INCIDENT; THE FO AND I THOUGHT THE ONLY POSSIBLE SCENARIO WAS THE FMC DUMPED THE DATA BECAUSE IT WAS ENTERED PROPERLY; VNAV WAS ENGAGED; AND IT IS POSSIBLE THAT THE DATA WAS LOST BECAUSE IT COULDN'T 'MAKE' THE DSCNT. THIS IS THE FIRST TIME THIS HAS EVER HAPPENED TO ME AND OTHER THAN THE FACT I SHOULD HAVE MONITORED BETTER; I HAVE NEVER SEEN AN FMS DO THAT. NOW I MONITOR BETTER AND CHK IT AGAIN BEFORE ALLOWING AND TRUSTING A COMPUTER TO DO IT.