It seems pretty unlikely that a 311 could possibly pull down against a 1 ohm resistor.
And then when that is fixed, measuring against such an extraordinary low reference voltage (12 microvolts???, really??) seems very unlikely.
The original post asked for detecting a drop of 50mV. But the schematic shows that the reference is 0.012mV, so there seems to be a fundamental problem here with scaling or units or something.
The reference voltage is so close to the "- rail" I don't think an antique device like 311 could even operate that close to the rail.
And it also isn't clear whether we are trying to detect an ABSOLUTE voltage drop, or a RELATIVE drop, and over what time period? This is why we typically use hysteresis here in the Real World.
Perhaps revealing the larger picture here would help us understand the project parameters.