pspice virtual gnd simulation
The basic problem is that your half rail generator is being dragged down to less than 2.5 volts by the dc offset on your source voltage. Then you have what appears to be a gain of 2 opamp circuit but the interactions of the source voltage superimposed on what is meant to be a steady 2.5 volts is screwing things up. Replace the two resistors of 100 ohm with a fixed dc voltage source is my advice.

By the way, with a gain of nearly 2 the opamp dc output voltage will be naturally centred a little lower than 4 volts and this, I believe is not what you want.