Going to try and keep this short and simple, got something to do soon so not being terse, just in a bit of a rush.
1/ The amount of CO2 in solution is directly related to the temperature and the pressure, here is the equation (
Braukaiser Carbonation Tables)
2/ At a given temperature the amount of CO2 in solution will in time form an Equilibrium (this is important). At equilibrium the same amount of CO2 is going into the beer as is coming out of the beer, they are Equal, so there is no net change. Remember that it takes time to reach an equilibrium. Change the temperature and/or the pressure and the equilibrium point will change.
3/ CO2 enters the beer through the surface, a full or nearly empty keg as the same interface area between the liquid and the gas above it. The Volume to be conditioned and the area through which gas can defuse is known Aera:Volume (A:V) in science its M^2 : M^3 (Squair meters to Cubic meters). More area to volume the system will move to equilibrium faster, and the converse applies. Shaking or using an airstone increases the area accelerating the movement of gas into/out of solution.
Those are the three main parameters. Alter any of them and the amount of CO2 in solution will change.
To keep the temperature fixed, make sure the thermostat on the fridge is reasonably accurate (holds to within 1-2oC). Fit a fan inside the fridge, this stops the formation of thermal layers which can easily be 5oC over the height of a fridge. Hasn't got to be very big a small computer fan is heaps.
Keeping the temperature homogeneous means you avoid the change in temperature that occurs as the beer level in the keg falls. If the fridge is colder at the bottom the beer in a less full keg will be colder than the top you will get increased CO2 in Solution.
The other really important factor is that as the level in the keg falls the gas interface aera changing the A:V so the changes in dissolved CO2 happens faster as the keg gets both Colder and as the A:V increases
Put in simplest terms, at a constant pressure -
Les colder beer, gas goes in faster
You are moving to a new higher equilibrium and further away from you target control point.
Put a little fan in the fridge.
Mark