The key to this simulation is the mesh and the quantity of convergence. Converging on the default 'delta S = 0.02' does not make much sense here. The port is always looking into an open so the S parameters do not change much at all from pass to pass causing premature convergence.
To solve this... First, seed mesh to 5mm on the plates. This needs to be done as this structure is nowhere near a resonance and the mesh will not be fine enough based upon lambda refinement. Second, Create an output variable for capacitance and converge on this quantity...now we are converging apples to apples. I get a capacitance of ~2.04 nF. If I want to get closer, I can by increasing the mesh seeding...
I attached the modified file...it is in HFSS13 and NO I will not make it available in any other version.
Have Fun