Widebody Transport
Flight Crew Air Transport Pilot (ATP)
ATC Issue All Types; Deviation - Altitude Excursion From Assigned Altitude; Deviation - Speed All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Weather / Turbulence
Flight Crew Took Evasive Action
Weather
We were just south of ALS (Alamosa) VOR at FL340 in level cruise flight; IMC; with moderate icing and moderate turbulence.  We started to see the airspeed start to bleed off from cruise mach. After setting max cruise power and still unable to maintain speed (at this point we had bled off about 10-15 knots of speed) I told the First Officer to notify Center that we would like to descend to FL320.  Because of the convective storm we were flying through; and radios were completely garbled; and we were unable to communicate.  I elected to start to descend to FL320 without ATC clearance after losing another 15 knots and within 20 knots of the lower foot.  At FL 330 we were able to talk to ATC and they gave us clearance to continue our descent to FL320.Possible mountain wave activity
Our airspeed dropped by over 40 knots indicated; putting us close to a possible aerodynamic stall. Even with max power; the airplane was unable to maintain or increase airspeed.
Air Carrier flight crew reported they were unable to maintain speed and altitude when they encountered mountain wave activity at FL340 in the vicinity of Alamosa VOR.