In the small signal gain calculations, you assume that the input signal is small enough so that it doesn't change the dc operating point of the device ( hence you assume a constant gm, ro..etc ), i.e. the circuit is linearized around the dc operating model ( a linear model is used to calculate the gain )
In large signal, the signal causes changes in the operating point. So, linearizing the circuit around the dc operating point would yield wrong results. In this case, a full non-linear model of the circuit has to be used.