Why are flight simulators bad at predicting drag and lift values at high angles of attack? (the nonlinear flow regime)
Laminar flow is easy. While there is a complete set of differential equations that describes any fluid flow, there is a wealth of simplifications and assumptions that you can use on laminar flow. This means that X-Plane doesn't need to model all the air around the wing, but can do the calculations based on wing profile and local velocities. Everything is relatively linear, so you can just change some variables and use predetermined parameters. Furthermore, it's completely time-invariant in steady state. You can now easily solve the equations, integrate the calculated pressure profile along the wing, and done!

For turbulent flow, none of that holds. The current way of simulating turbulent flow is to do a Finite Element analysis or similar (e.g., FDM). Basically, you will need to consider all the air in a large volume around the wing, divide it up in a small grid and simulate it. For a good calculation, this takes in the order of seconds to minutes for a single 2D cross-section on my pretty decent laptop. And then we're neglecting the 3D influences. Furthermore, turbulent flow changes w.r.t. time. For example, open your car window on the highway - you will hear the wind roar and pulsate. This means that you will need to get your previous pressure- and velocity field, and use that as a starting point for your next FEM/FDM analysis. Finally, turbulent flow is extremely hard to predict correctly, even with above methods: a slightly rougher surface, a small bolt or a small wind gust can delay flow separation for a few inches, completely invalidating your results. Perhaps this YouTube video (note: this is not simulated in real time!) might shed some light on the vast complexity and time-dependency of turbulent flow - and remember that your horizontal stabilizer will see disturbed air in stall conditions, making it necessary to simulate the entire flow field around the airplane for a correct simulation, not just the wing sections. 

Of course, X-plane has a framerate measured in frames per second, not frames per hour. This means that they use a bunch of assumptions to calculate the wing lift. I'm guessing they just have some values for location of flow separation and turbulent pressure for some fixed velocities and angles, and interpolate to the actual values. My guess is that they also have some parameters that aren't actually calculated, but are chosen such that some very basic maneuvers are possible like spin recovery, regardless whether these values correspond to any actual physical phenomena - it's a game, after all.