A B737-800 FLT CREW EXCEEDED THE OPERATIONAL LIMITS OF THE FLAP SYS WHEN EXTENDING FLAPS TO 1 DEG AT FL370 DURING A LOSS OF AIRSPD NEAR TSTM ACTIVITY ON FREQ WITH ZDV; CO.

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THE FLT APCHED A SCATTERED LINE OF LOWER ALT CELLS WITH US NEAR THE TOPS. ATC NEEDED US TO DEVIATE S; WHICH WE DID. THE ACFT WAS SLOWED TO TURBULENT PENETRATION SPD WITH ALL FLT ATTENDANTS AND PAX SEATED. WE WERE AT A SAFE DISTANCE BTWN CELLS WITH PRACTICALLY NOTHING PAINTING ON RADAR BTWN. WE ENTERED THE CLOUDS AND THE TURB BEGAN. IT INCREASED FROM LIGHT TO MODERATE. THE B737-800 HAS A TENDENCY TO SPD UP IN TURB; BUT THIS TIME IT DECREASED. THE AUTOTHROTTLES WERE AT MAX CRUISE PWR BUT THE IAS; THOUGH BOUNCING AROUND; STEADILY DECREASED. MAX CONTINUOUS PWR WAS SELECTED TO NO AVAIL. SOON ON THE FMS SCRATCH PAD 'BUFFET WARNING' WAS INDICATED. THE CAPT EXTENDED THE FLAPS TO 1 DEG HOPING TO LOWER THE STALL SPD. THE SPD CONTINUED TO DECREASE AND THE CAPT COMMANDED I BEGIN A DSCNT; WHICH I DID. HE IMMEDIATELY TOLD ATC WE WERE DSNDING. ATC HAD US TURN R FOR TFC; WE DID. AFTER DSNDING 3000 FT; THE AIRSPD FINALLY BEGAN INCREASING ENOUGH TO RAISE THE FLAPS AND CLB BACK UP TO ALT. WE RPTED THE TURB AND CONDITIONS TO ATC. THE ACFT HAS A LIMITATION; MAX FLAP EXTENSION ALT OF 20000 FT. NORMALLY; THE MAX EXTEND AIRSPD IS 250 KTS. I THINK THE CAPT THOUGHT THAT WE WERE SO FAR BELOW THAT SPD; AROUND 200 KTS; IT WOULD BE OK TO EXTEND THE FLAPS TO HEAD OFF A POTENTIAL STALL. LOOKING BACK; WE SHOULD HAVE DSNDED EARLIER. WE ALSO SHOULD HAVE CONTACTED OUR DISPATCHER; MAINT AND OPS DUTY OFFICER. THE CAPT DID WRITE THIS EVENT UP AND SENT IT THROUGH INTER-COMPANY CORRESPONDENCE WHERE MANY DEPTS WOULD SEE IT.