LGT MISSES XING RESTRICTION. NOTIFIES ATC; NEW CLRNC ISSUED.

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FLT HAD BEEN GIVEN AN INITIAL XING RESTRICTION OF 'CROSS MARRC INTXN AT FL190.' OUR FLT MADE THAT XING RESTRICTION WITH NO PROB. SHORTLY THEREAFTER; THE CAPT OF THIS 2 MAN CREW LEFT THE ATC FREQ TO ADDRESS THE PAX AND ANSWER A QUESTION FOR THE LEAD FLT ATTENDANT; WHO HAD ENTERED THE COCKPIT DURING THIS TIME FRAME. DURING THE CAPT'S ABSENCE FROM THE FREQ; ATC HAD ISSUED A XING RESTRICTION OF 'CROSS VIBES AT 13000 FT;' WHICH THE FO ACKNOWLEDGED AND RELAYED TO THE CAPT. I BELIEVE THE CAUSE OF OUR BEING UNABLE TO MAKE THE VIBES XING RESTRICTION WAS DUE TO A COMBINATION OF FACTORS. FIRST; LET IT BE KNOWN THAT WE IMMEDIATELY CONFESSED OUR INABILITY TO MAKE THE XING RESTRICTION AT VIBES INTXN. CONTRIBUTING FACTORS INCLUDE: CAPT OFF ATC FREQ WHEN CLRNC WAS ISSUED. FO THOUGHT CAPT HAD FULLY ACKNOWLEDGED AND UNDERSTOOD THE NEW XING RESTRICTION. LEAD FLT ATTENDANT ENTERING THE COCKPIT WITH DISTR. EXCESSIVE TAILWINDS AT OUR ALT; 80 KTS PLUS. AUTO FLT SYS ON THIS ACFT WAS EXCEPTIONALLY SLOW TO REACT TO DSCNT INPUT (VNAV) AND WAS SLOW AT ALT CAPTURE; OVERSHOOT OF LEVEL OFF BY AS MUCH AS 400 FT. JUMP SEATER IN THE COCKPIT (SLIGHT DISTR). FINALLY; ATC WAS MORE THAN FORGIVING AND ACCOMMODATING WITH OUR DILEMMA; AND ISSUED A NEW XING RESTRICTION OF 'CROSS LIZZI INTXN AT 11000 FT.' NO FURTHER INCIDENT WAS INCURRED; BUT THIS CREW WAS MOTIVATED TO SHARE OUR EXPERIENCE.