ACR MDT FAILED TO START DESCENT WHEN CLEARED BY APCH CTLR.

Narrative

ACFT WAS IN CRUISE MODE WAITING FOR AN APCH CLRNC. ORD APCH CTL ISSUED US A CLRNC TO DSND FROM 7000 TO 4000' AND INTERCEPT RWY 14L LOC. F/O WAS PF AND I SET 4000' IN THE ALT ALERTER AND ARMED THE INDICATED AIRSPD MODE TO ARM THE FLT DIRECTOR FOR A DSCNT. I THEN TURNED MY HEAD TO GET AN APCH PLATE READY FOR A PERIOD OF APPROX 1 MIN. I THEN TURNED MY ATTN BACK TO THE AIRPLANE APCH CTL CALLED ME AND TOLD ME TO DSND 'NOW' TO 4000'. THE F/O HAD NEVER LEFT THE ALT OF 7000'. THE F/O THEN WENT FLT IDLE ON THE PWR AND WE DSNDED TO 4000'. THIS WAS OUR NINTH LEG OF THE DAY AND HAD FLOWN INTO ORD 4 TIMES. FATIGUE LEVEL WAS HIGH AS WE WERE ENTERING OUR THIRTEENTH HR OF DUTY TIME. ON TOP OF THIS WE ONLY HAD REDUCED REST OF 8 HRS THE PREVIOUS NIGHT; WHICH TRANSLATES TO ABOUT 5 1/2-6 HRS OF SLEEP AT THE MOST. THIS REDUCED REST WAS SCHEDULED INTO THE TRIP PAIRING. I SINCERELY BELIEVE THAT HAD WE GOTTEN AN 8 HR PERIOD OF SLEEP MAYBE THIS ALT DEV WOULDN'T HAVE HAPPENED. I ALSO THINK THE 9 LEG DAY; 13 HR DUTY DAY; AND FLYING INTO THE WORLD'S BUSIEST ARPT 4 TIMES THAT DAY CONTRIBUTED.