An instructor and student pilot aboard a C172 were unable to maintain altitude in downdrafts and turbulence over the North Rim of the Grand Canyon. Had to reverse course to regain flight path control and return to their IFR altitude.

Narrative

My instructor and I were over the North Rim of the Grand Canyon mountain range at 11;500 MSL when we encountered moderate turbulence and a strong downdraft. Our ground speed was down to about 20 KTS; and the rate of descent was over 1;000 FPM; we were unable to maintain altitude and got below the assigned altitude by at least 1;500 FT. We advised ATC of the problem; but the quality of the radio reception was deteriorating; and we could not hear whether we were given an amended clearance for a lower altitude. We reversed the course; flew out of that area; climbed back to the initial altitude of 11;500 FT and contacted ATC. We requested to return back to PGA and received clearance from Denver Center. Prior to that flight we checked the weather; and the winds were calm at the surface and about 30 KTS at 12;000 FT MSL; VFR; no significant weather. We were not familiar with the wind patterns over mountain ranges. This event could have been prevented by obtaining knowledge of mountain flying and the potential dangers that can be encountered. The second time we deviated from ATC instructions was on the way back to PGA. We were both nervous after having encountered an uncontrolled descent into terrain a few minutes ago. We were cleared for a visual approach to Page airport. I didn't know that 'cleared to land' didn't mean that we could switch the frequencies. I switched us to CTAF. My instructor did not notice my mistake either. After we landed; we called FSS and were told that Denver Center were 'looking for us'. Both deviations could've been prevented by better flight planning and CRM.