Why not maintenable. Even if the plane have a constant thrust (RPM), it is can manuevering to the higher altitude and stay at that altitude with the same machine power.
Because typically planes do not have enough thrust to overcome their weight.
Instead they use lift.
Lift is dependent upon the air pressure. If you have a much lower air pressure then the lift will be much less.
Also, the thrust is also dependent upon air pressure.
And if they kept flying in a straight line, they would have a higher angle of attack, and thus less lift.
What is the mechanism for constant adjustment?
For manual control they use the yoke.
For autopilot it is the autopilot.
Again, they don't just try to remain straight relative to their starting point.
They try to maintain the desired attitude and altitude and so on.
If either the pilot or the autopilot notices they are flying to high, they adjust to correct. If they are flying too low, they adjust to correct. If their pitch is wrong, they adjust to correct.