BEECH JET 400 FO FAILED TO MAINTAIN SPD ASSIGNED SPD OUTSIDE THE OM AFTER BEING CLRED FOR THE APCH.

Narrative

AFTER OUR DEP FROM SSI; WE LOST OUR FMS NAV. ACCORDINGLY; WE ADVISED ATC AND REQUESTED VECTORS TO OUR FIRST FIX. FROM THERE; WE HAD TO USE VOR NAV AND OUR BACKUP NAV ON OUR SECONDARY DISPLAY UNIT (SDU). THE ENRTE TRIP WAS IMC; AND OUR WORKLOAD WAS GREATLY INCREASED. AS WE BEGAN TO FLY THE ILS RWY 9R; WE BEGAN TO REVIEW AGAIN THE ALTS AT THE VARIOUS MILEAGE FIXES ON THE APCH. WE HAD TO USE OUR BACKUP SDU TO SHOOT THE APCH (TO GIVE US BOTH VERT AND HORIZ GUIDANCE). THE SDU WAS SET TO THE ILS FREQ. WE HAD THE VOR SET TO ATL. MY COPLT HAD HIS HANDS FULL FLYING THE APCH IN BAD WX. I WAS COMMUNICATING; CALLING FOR CHKLISTS; AND VERIFYING ALTS AND DISTANCES. WHEN WE WERE CLRED FOR THE APCH; WE WERE GIVEN 180 KIAS TO MAINTAIN UNTIL THE MARKER. I NOTICED WE HAD SLOWED CONSIDERABLY. AS I REMINDED THE PF TO KEEP HIS SPD UP; SO DID ATC. WE LANDED WITHOUT FURTHER COMMENT FROM ATC. WE EARNESTLY DID EVERYTHING SAFELY AND AS INSTRUCTED; HOWEVER; WITH OPTIONS (EQUIP AND WX) TAKEN AWAY A ROUTINE APCH BECOMES EXTREMELY DIFFICULT.