I was flying around kyrat so I decided to go through the mountains to the fortresses not yet conquered using the buzzer. But every time I try to do that, he whistles and starts to fall. Why does it happen? Is this why I have not yet unlocked the map part or another reason?
From what I remember when I played this game, the Buzzer has a maximum altitude that it can reach. Once it surpasses this altitude, it will set off an alarm to warn the player that it is about to stall out. If it stalls, it will begin to fall to the ground.
From the Wiki page:
The Buzzer can fly at moderate altitudes (above most Bell Towers), but at high altitudes a light on the dashboard will blink, accompanied by an alarm to warn the player that they are flying too high. If the player continues to fly upwards, the Buzzer's engine will fail, causing the helicopter to succumb to gravity and if the engine is not restarted and power regained, the buzzer will crash and perhaps explode, killing the player.
Based off your question, it seems you are flying too high with this vehicle in the mountain area.