Not sure if it will help but there is a wiki article about the 96 and some internal pots that can be adjusted. It sounds semi related to your problem.
Make sure and read the thread that is listed in the wiki link as well.
If you do adjust the pots, do mark them first with a fine marker so you can return them to the original settings if you do not notice a change.
That is important.
The wiki is here:
PRO-96 Internal Adjustments - The RadioReference Wiki
Hope this helps!
A lot of the tuning in the 96 is done by spreading the coils you will see in the picture that are covered with wax. You either spread them apart or squeze them together to adjust the PLL frequency. That does require test equipment so don't mess with those or the other transformer slugs in the metal cans as doing so could really take the radio off frequency to where it would not work at all.
Adjusting the pots highlighted in the picture is not that risky as long as you mark them first.
Post back if that works or not if you try it even.
Mine has never needed any alignment but it seems many others have had issues like yours and those pots brought them back on frequency.
I'd swear I just read another thread on this very subject here the other day as I think that is why I found that wiki article in the first place. I cannot recall the thread though but I think someone explained the functions of the three pots in greater detail.
