XING RESTR NOT MET. FMS FAILURE.

Narrative

AT FL310 INBOUND TO ABQ VOR; CLRED TO CROSS 45 SW OF ABB AT FL240. FO PROGRAMMED FMS TO ACCOMPLISH THIS XING RESTR. FO DID NOT MANUALLY TUNE TO ABB. I WAS USING MY VOR/DME TO FIND A VOR COMBINATION FOR THE FMS TO TUNE. WE WERE DOWN TO 2 FMS DME STATIONS AND OCCASIONALLY DOWN TO 1 VOR/DME STATION. THE FMS; HOWEVER; SHOWED OUR POS AS WELL AS TOP OF DSCNT AND END OF DSCNT (AT 45 SW OF ABB). AT ABOUT 60 DME SW OF ABB (FMS MAP) IN THE DSCNT; CTR ASKED US TO STOP THE DSCNT AT FL290. ABOUT 30 SECONDS LATER THE FMS MAP FAILED (WITHOUT WARNING). CTR THEN TURNED US TO A NW HDG AND ASKED US OUR DSCNT CLRNC AND OUR DISTANCE FROM ABB. I MANUALLY TUNED ABB AND WE WERE ABOUT 46 DME SW OF ABB. I ASKED CTR IF THERE WAS A CONFLICT AND WAS TOLD THAT THE STOPPED DSCNT AT FL290 AND THE TURN OFF COURSE PREVENTED A CONFLICT. WE WERE UNABLE TO RECOVER FMS FOR REMAINDER OF FLT. FACTORS AFFECTING THIS PROB: 1) UNEXPLAINED AND UNEXPECTED FMS FAILURE. 2) ONE CREW MEMBER NOT MANUALLY TUNING OF ABB VOR AS A BACKUP. 3) ACCEPTING FMS DATA FOR NAV (HOWEVER; IS THIS NOT A SYS CERTIFIED FOR ACCURATE RNAV). 4) TOO MUCH TRUST IN THE AUTOMATION FOR 100 PERCENT RELIABILITY.