I have found a 12" x 4" junior whitehead PJT on Google, you don't say how long you have owned this machine.
If This is the model this is a really substantial machine.
I am not familiar with the single post bed, not having worked on any, but have maintained the usual 4 corner type as a wadkin etc type, much on a monthly basis.
As you're probably aware, as both beds rise and fall, you can re sharpen the blades, in the block, 2, or 3 times between cutter changing, and setting the outfeed table, or bed to the new cutter height
With this thickness problem, Easiest is to look for the obvious and simplest reasons for this happening.
As I can't see any rise and fall wheel, I presume the thicknesser bed does not have rollers fitted, to worry about.
As I, and others, have said, First thing I would check would be the beds, Are they co planer with each other.
where they slide in and out, are there any shims, and is there any dirt lifting the table one sided, that the cutters are set to, as 0.5mm could easily be lost, or gained.
I would hope the bed workings are all within the guard at the rear, but with a single post I find it difficult to attribute the problem to cogs and backlash giving on to one side misalignment, that you are experiencing.
Cutter block bearings Peter mentioned, is a possibility.
Regards Rodders