Why does the intensity of an action potential once generated at the trigger zone remain undistured throught the axon?
Actually, it would be better to say that action potential does not travel but is regenerated anew in a sequence along the axon.


I would like to elaborate how this happens and why this is the reason why the action potential stays constant:

In rest state, there is an ion gradient across the membrane of each cell. This causes a small voltage between the outside and the inside of the membrane, the so called transmembrane potential.
Once the cell membrane becomes permeable for ions (normally this occurs when an ion channel is opened), the potential causes ions to flow across the membrane, the membrane becomes depolarized. 

In the axon, the membrane contains so called voltage-gated ion channels. As soon as the membrane is depolarized at the trigger zone, the depolarization of the adjacent membrane causes voltage gated ion channels to open in that adjacent memrane as well, causing ions to flow also across the adjacent piece of membrane. This process continues in a wave along the whole membrane, this is what we call the action potential. Because the ion gradient across the membrane and the density of ion channels is constant along the whole axon, the amplitude of the action potential stays constant along the whole length of the axon.