In plotting functions Mathematica makes a determination of how much of the function to show according to some algorithm that determines where the interesting parts of the function are. To override this use the PlotRange option. In your case this will show the full graph:
Plot3D[{(c^2*Pi)/(x^2*Pi)}, {x, 1, 3}, {y, 0, c},
RegionFunction -> Function[{x, y, z}, 0 <= y <= x - c],
PlotRange -> All]
