Schmitt trigger not working
Could be any combination of several things:
You do not re-establish a stable DC reference voltage for the signal after the lowpass filter.  The 1.2 K resistor has a capacitor on each end.  As a start, add a 1 M resistor to GND in parallel with the 1.2 nF LPF capacitor.
The LT1719 is not a normal comparator, and has its own internal hysteresis.  Why are you adding additional hysteresis around it?
Separate from that, with it running on +/-5 V, the two externally set trip points are +/-326 mV.  (Maybe - I have not worked through the output stage configuration.)  That is 0.652 V peak to peak, which is greater than the input signal.