I've done a wee bit of work with Neon signage.
How old is the sign in question?.
There are a number of things that could be causing the last letters to dim.
Firstly, a lower voltage output from the Secondary side of the transformer(s) feeding the letters, will cause the light output to drop.
A poor grounding connection on one side of the Secondary winding will have the same effect.
Are the transformers centre-tapped?, if so, check these connections too, there should be a good ground connection at these points.
The reason I ask about the age of the sign, is because, the last letters may be the original parts, where the other letters may have been replaced earlier on in the sign's life.
Neon signs usually have some form of a Phosphor coating on the inside of the glass(not unlike a Fluorescent tube), as this coating "wears out" the tubing gets dimmer, but this usually takes years.
I would say that you probably have a bad connection somewhere in the system.
Hope this helps!.