Andy,
As the air is less dense you're physically moving faster for a given ammount of drag. This means more power is required.
However, since the air is less dense, you don't actually need any more thrust.
When IAS is fixed, you are talking about flying with a fixed value for the 1/2 rho V^2 bit of the lift and drag formulae. As you climb, as rho (air density) is decreasing, then your aircraft must be increasing in V, (which is TAS).
Remember, IAS isn't really a speed, in the proper 'Physics' sense of the word. The only one out of IAS/RAS/CAS/EAS/TAS etc that is truly a speed is TAS, and thats what the V is in the lift formula.
This is why aircraft handle depending on IAS, but Navigate based on TAS.
Topics such as stability or Prop efficiency depend on both the 'IAS/RAS/EAS' bit (for aerodynamic forces) and also the 'TAS' bit with regards to the geometry of the physical motion of the aircraft.
pb