What exactly happens when power is reduced in trimmed, straight and level flight? I understand that trimming an aircraft at a particular airspeed e.g. 100kts will keep the aircraft flying at that airspeed (100kts) even if you were to e.g. Lower power. This is apparently accomplished by the pitching down of the trimmed aircraft.

But I am not too sure if I understand the rationale behind the pitching down. I hope to seek advice on whether what I understand is correct: 

When you elevator trim to fly unaccelerated straight and level flight (all forces balanced) at e.g. 100kts, you are relieving the pressure needed to keep your aircraft in that angle of attack that produces enough lift to counter the weight, at that particular airspeed (because any increase or decrease in airspeed also will affect lift, so speed will affect the amount of lift that needs to be created by the AOA to counter the weight so as to stay level). So if your speed starts to drop, the amount of lift that your AOA must make = increased. But since you have trimmed elevator to that position means the AOA is fixed. So what happens is that the aircraft will pitch down (trade height which is potential energy for kinetic energy so your speed increase), then your speed will be back to what it used to be and your that trimmed AOA will continue to be able to supply that exact amount of lift, which together with the lift at that same airspeed is just right to counter the weight. So the aircraft will be back to level flight again.

Since power is lowered, I would expect the aircraft to continue to lose speed and the whole cycle of pitching down then back to straight and level will go on and on.

Does this make any sense?
This makes sense and is approximately what happens if you reduce thrust during trimmed straight and level flight. The aircraft will go though a series of damped oscillations, called 'phugoid' until it finds its new equilibrium state. The new state will be the original airspeed, but now in a constant descent.