Positive and Negative Sense Circuit. How/why does this work?
Probably just an issue with the model in LTSPICE, coupled with the fact that op-amps use the difference in the currents being pulled out of or inserted into the pins. Since one pin is floating here, no current is going either way. That is not how you should use them though, since any noise in the system will couple into the input.

However, why are you even using one, just power both from +-5V and switch the inputs around on U1 and feed the output to the other diode, D3. 







simulate this circuit &ndash; Schematic created using CircuitLab

The circuit would also be more accurate if you used resistors instead of the diodes in your reference, assuming the 5Vs are regulated properly.