CE560 CREW DSNDING ON THE COATT 4 ARR TO HEF DOES NOT QUITE MAKE XING RESTR.

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WE WERE DSNDING ON THE COATT 4 ARR FOR THE HEF ARPT. ZDC ISSUED A XING RESTR OF 'CROSS FALKO AT 10000 FT 250 KTS.' AS A CREW; THIS RESTR WAS ADDED INTO THE VERT NAV FOR A 2200 FPM DSCNT. ONCE REACHING OUR TOP OF DSCNT POINT; THE PLANE BEGAN A DSCNT FOR FALKO AT 10000 FT 250 KTS. DSNDING THROUGH FL190 WE AS A CREW BEGAN THE DSCNT/APCH CHKLIST. WE EXPECTED THE VISUAL APCH TO RWY 34R AT HEF; SO THE VISUAL APCH WAS LOADED (RNAV RWY 34R HEF). ONCE APCH WAS ENTERED; THE FMS DISCONNECTED THE VNAV AND REMOVED FALKO FROM OUR RTE PAGE. NOTICING THIS; WE RE-ENTERED FALKO AND THE ERASED ROUTING; SELECTED VERT SPD MANUALLY WHICH NOW REQUIRED A 4500 FPM DSCNT AND FLT IDLE TO MEET THE XING RESTR. IT APPEARED WE WERE NOT GOING TO MEET FALKO AT 10000 FT. BEFORE WE COULD ADVISE ATC; THE CTLR SAID 'ACFT X YOU WERE SUPPOSED TO CROSS FALKO AT 10000 FT.' WE ADVISED ATC WE WERE 'OUT OF 11000 FT' WITH APPROX 4 SM TO GO. FOR FUTURE REF; LIMITING THE USE OF THE VNAV SYS TO THE ENRTE PORTION OF FLT; ALONG WITH SELECTING V-SPD FOR TRANSITIONING; WILL ELIMINATE THIS PROB FROM OCCURRING AGAIN.