Duane, Open a pose file in a text editor.

every actor has six enties x/y/z rot The rotations - the joint movements
there is also x/y/z/ trans The transitions - slide up/down - side/side - back/forth

Unless the autor is particularly devious, poses are done on figure with the eyes at x/y/z trans = k 0 0.

Now, if you have just spent 15 minutes getting the R eye on a morphed face xtrans = k 0 -0.0005 , as best,
any pose you apply will change it to k 0 0
everything you did is gone. Now, I think you have tried to fix this in the past by making a morph of the trans position for each eye and supplying it with a face morph.

The morphs are already there. They are called "trans".
It is just that you must "lock" the values, so no pose can change them.

Easier is to:
forcelimit 4
min -0.0005
max -0.0005
{
k 0 -0.0005
}

for this right eye xtrans
the forcelimits 4 means that this value will stay even if
"use limits" is unchecked in Poser

In this case the k 0 -0.0005 is probably not necessary, because with min = max = -0.0005 and forcelimits 4
the channels cannot be anything but -0.0005
even if you made k 0 100 , it would still be -0.0005

You can set everything but forcelimits from within Poser.
forcelimits to 4 must be done using a text editor.

The difficult part of this, is that I learned this from tips from others and then experimenting on the files in a text editor and seeing what it does in Poser. You remember what not to do much better when you see the blowup, rather than reading a rule from someone who did.

added stuff:

A value of MORdonor faces poses is that the trans settings for each eye can be added into the pose file - in a locked setting. A face pose that sets V2/M2 morphs can also do this. Not by Poser for you though, TE work.
But, if you do this for one, you have to do it for all, or else have a pose file that just sets the eyes back to zero, for those faces where this is correct. One a dial is locked, it will stay locked until you change the values.