CRJ700 FLIGHT CREW IS JARRED FROM THEIR REVERIE AT FL370 BY THE AUTOPILOT DISENGAGING AND THE STICK SHAKER COMING ON.

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IT WAS THE CAPT'S LEG AND WE WERE LEVEL AT FL370. WHILE LEVEL; THE SPD BLED DOWN; THE AUTOPLT KICKED OFF; AND THE STICK SHAKER CAME ON. I IMMEDIATELY PUSHED THE THRUST LEVERS TO MAX AND THE CAPT WENT TO THE CTLS. THE ACFT BUFFETED SLIGHTLY AND WE SLOWLY DSNDED BTWN 200-400 FT WHILE THE PLANE GAINED SPD. I THEN ASKED ATC FOR FL350 AND THE ALT CHANGE WAS APPROVED. I FEEL THAT THE CAUSE WAS A COMBINATION OF THE PF NOT PAYING CLOSE ENOUGH ATTN AND POSSIBLE WINDSHEAR AT ALT. WE HAD BEEN FLYING AT FL370 FOR QUITE A WHILE WITH THE THRUST SET TO HOLD MACH .77 WHEN SUDDENLY THE AUTOPLT KICKED OFF AND THE STICK SHAKER CAME ON. THERE WAS A DIRECT TAILWIND ON THE ACFT BTWN 120-130 KTS AND LIGHT CHOP; WHICH MAKES ME THINK THERE MAY HAVE BEEN SOME OUTSIDE FACTORS INVOLVED IN OUR SITUATION. SUPPLEMENTAL INFO FROM ACN 813640: WE HAD CLBED TO OUR INITIAL CRUISE ALT OF FL370. THE AIRPLANE WAS STABILIZED IN CRUISE FLT AT MACH .77. THE AIRPLANE WAS ALLOWED; THROUGH LACK OF ATTN OF THE CREW; TO INADVERTENTLY SLOW TO AN UNSAFE SPD FOR THAT ALT. THE AUTOPLT DISCONNECTED AND THE AUTOMATIC IGNITION ACTIVATED. THE THRUST LEVERS WERE ADVANCED TO CLB PWR AND THE AIRSPD STABILIZED. WHILE HOLDING FL370 AND WAITING FOR A REQUEST FOR A LOWER ALT; TOO MUCH BACK PRESSURE WAS APPLIED ON THE YOKE AND THE STICK SHAKER ACTIVATED. WE WERE THEN GIVEN A LOWER ALT OF FL350. WE DSNDED AND ACCELERATED BACK TO THE CRUISE SPD OF MACH .77. HUMAN FACTORS THAT CONTRIBUTED TO THE EVENT INCLUDED FATIGUE AND EMOTIONAL STRESS OF THE CAPT AND THE FO'S LACK OF ATTN. THE NIGHT BEFORE THE EVENT; THE CAPT DEALT WITH A PERSONAL MATTER CONCERNING A CLOSE FRIEND WHOSE WIFE HAD BEEN HOSPITALIZED. THE CAPT DID NOT RECEIVE AN ADEQUATE AMOUNT OF SLEEP BEFORE RPTING TO WORK. ONCE THE ACFT REACHED CRUISE ALT AND THE SPD WAS STABILIZED; THE CAPT XFERRED CTL OF THE AIRPLANE TO THE FO. THE CAPT CLOSED HIS EYES TO REST. MOMENTS LATER THE AUTOPLT DISCONNECTED AND THE CAPT TOOK CTL OF THE AIRPLANE. WHEN THE CAPT RE-TOOK CTL OF THE ACFT; HE TOOK NOTE THAT THE FO HAD CHARTS IN HIS LAP AND WAS DOING HIS CHART REVISION; AND HAD NOT BEEN MONITORING THE ACFT AND WAS UNAWARE THAT HE LET THE AIRSPD DETERIORATE. THE FLT PROCEEDED SAFELY TO THE DEST CITY AND THERE WAS NO FURTHER INCIDENT.