Does the positive and negative half cycle of an AC source sees different resistance?
The input capacitor is making it a little difficult to see what's happening so let me say one thing; when the external input signal is below 0 volts, the DC level at the base is still a positive due to the bias resistors R1 and R2 AND, the signal superimposed on the base DC bias never gets down too low i.e. it always keeps the base emitter junction forward biased. The input capacitor ensures that you can pass a supposed AC current into the base node whilst preventing that node going negative or below around 1 volt in normal operation.
Clearly, if you overdrive the input then serious distortion occurs and the base emitter region gets fully reverse biased - when this happens the base collector region is still reverse biased (as per normal operation) and the input impedance would be see to rise slightly.