nanoPower comparator driving MOSFET not providing expected output
First of all:


  The MAX9060 and MAX9061 have open-drain outputs  


so it will never drive M1. You need to add a pull-up resistor.

EDIT:
As OP indicates, the MAX9064 is used which has a push-pull output.  

My first thought was M1 has too much leakage current, pulling down the output of MAX9064.
However, the Gate to Source Leakage Current of the MCH3484 is at most 10 uA at \$V_{GS}\$=4V, and with lower \$V_{GS}\$, it will be even less.
According the MAX9064 datasheet, at (test conditions) \$V_{CC}\$ = 1.2V and \$I_{SOURCE}\$ = 40μA the ouput voltage is typically 1.12V or min 1.0V. So with a lower \$I_{SOURCE}\$, it will indeed be enough to drive the MAX9064.

Regarding measuring an output while switched off
You probably measure a voltage due to the Zero-Gate Voltage Drain Current of M2. It is in the order of uA (at VDS=−12V, VGS=0V it is −10 μA) which will cause a voltage  across the measurement resistor (which is in the order of MOhm) of the multimeter.
Apply a 1kOhm resistor as load and you should measure nothing.