AN A319 CREW FINDS THEIR ACFT SLOWING TOWARD STALL SPD AT CRUISE ALT. UNABLE TO MAINTAIN ALT; THEY COORDINATE WITH ATC FOR DSCNT. AUTOFLT SYS IS FOUND TO BE IN THE APCH MODE.

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THE CAPT WAS THE PF. ONCE WE LEVELED OFF AT FL350; AFTER CLBING FROM FL310; THE ACFT ENGS WERE APCHING IDLE THRUST AND THE ACFT BEGAN TO DECELERATE. WE WERE NOT SURE OF THE PROB; SO THE CAPT INSTRUCTED ME TO ASK CTR FOR A LOWER ALT AND HE BEGAN A SLOW DSCNT TO TRY TO PREVENT A STALL SIT. CTR ADVISED A LOWER ALT WAS NOT AVAILABLE DUE TO TFC AT FL330. WE ASKED FOR A TURN AND CTR ASKED IF WE WERE DECLARING AN EMER. THE CAPT SAID NO. I SOON REALIZED THAT THE ACFT AUTOMATION WAS IN THE APCH MODE WHICH IS WHY THE DECELERATION OCCURRED. I REASSURED THE CAPT THAT THE SPD SHOULD NOT DETERIORATE TO A DANGEROUS SIT AND TOLD HIM TO MANUALLY SELECT SPD MODE. THIS WAS SUCCESSFUL AND THE ACFT ACCELERATED AND THE CAPT INITIATED A SLOW CLB BACK FROM FL341-343 BACK TO FL350. ONCE AT FL350; THE CAPT SET THE AUTOMATION BACK INTO CRUISE MODE AND THE FLT CONTINUED WITHOUT INCIDENT. WE DO NOT KNOW WHAT CAUSED THE AUTOMATION IRREGULARITY. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THAT IT TAKES 5 KEYSTROKES TO PUT THE AUTOFLT SYS INTO THE APCH MODE. HE FELT THAT IT WAS NOT PUT THERE INADVERTENTLY BY THE CREW. HE ALSO RPTED THAT IN THE ORIGINAL COCKPIT PREPARATION HE ROUTINELY USES WET TOWELS TO CLEAN UP THE COCKPIT. THIS DAY HE FOUND SOMETHING STICKY ON THE FMS CTL HEAD. HE CONCLUDES THAT THIS MAY HAVE BEEN THE CAUSE OF THE PROB. EITHER THE PREVIOUS SPILL OR CONTAMINATION OR THE MOISTURE THAT HE MAY HAVE INTRODUCED IN THE CLEANING PROCESS.