op-amp pin is sitting at high voltage (active low-pass filter)
The OP1177 data sheet says that the input voltage range for the device is -3.5 volts to + 3.5 volts when powered from a +/- 5 volt supply. This means any input closer to the op-amps negative rail than 1.5 volts is going to hit problems. Your negative rail is 0 volts and your positive rail is 5 volts hence the usable input range is from +1.5 volts to +3.5 volts. 


  I have a gain of ten but I get a minimum input voltage of ~160mV


Your signal tries to fall to 0 volts and the op-amp will possibly restrict that from happening due to exceeding the specified input voltage range at the negative rail. All bets are off when you try and do things like this.

In addition to this the data sheets informs that the output signal can only get to within about 1 volt of the negative rail (or +1 volt in your set-up).


  I am going to change to a LT1001 op-amp which runs without this
  problem in simulations


That device will have similar problems - it's input range gets to within 1 volt of the negative rail typically but is not guaranteed to operate under all circumstances unless it gets no closer than 2 volts. The output voltage swing is guaranteed to within 3 volts of the rails but no closer.