There are two problems here. First, the FMs need revision as almost no single aircraft in the sim can attain its historical performance values. According to the latest Friday update the developers are working on the FM, so a future patch will probably correct that.
Second, there is an operational error involved: you are flying at full fine pitch.
The best thing you can do is trim the aircraft to fly at about 250 kph (i think that's the best climb speed in the 109) and then add power to make it climb (the nose will rise to maintain 250kph and you will climb).
The higher you go, the lower the outside air pressure is and that means lower pressures inside the engine intake manifold as well: your Ata gauge will drop as you climb.
This means that you can add some throttle to bring it back up (i like to climb at about 1.2 Ata and loiter at 1.0 Ata to save fuel) and after a certain altitude not even full throttle will give you the full Ata you can get at ground level.
Now for the prop. Assuming you are cruise climbing like described, it's not efficient to climb at full fine pitch. 12:00 pitch is like 1st gear in a car: it pulls the car uphill with ease but it doesn't let you attain a high speed.
Similarly, full fine pitch is good for low speeds and high angles of climb (eg, at the top of a zoom climb in combat), or when you want to keep your speed under control and the engine responsive (eg, during approach and landing).
In fact, the higher you go you need to coarsen the pitch, because the outside air is thin and the propeller doesn't "bite" well at fine settings: it just turns really fast but doesn't generate much thrust.
Depending on how steeply i climb, i usually set the pitch between 10:10 and 11:00, coarsening a bit as i go to higher altitudes. Of course, if you coarsen it too much there is again a problem, because the propeller has more resistance and after a point the engine can't turn it efficiently.
It's a balancing act, you just need to play around with it and get a feel for it.
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