How to avoid voltage drop on undervoltage protection circuit?
I would replace Q1 by an enhancement PMOS with low gate threshold and low RDSON value. 

Then the changes in the circuit would be to replace R6 by a short circuit as it would not be necessary anymore.

There are two ways of connecting the MOSFET, shown in the schematics below. Option A is the classic one, or the Option B. The Option B advantage is that it provides protection against reverse polarity of the battery. You can read an explanation of its working mechanism in http://www.ti.com/lit/an/slva139/slva139.pdf (figure 3). 

The disadvantage of using Option B in your circuit is that even when the channel is OFF, there is a diode voltage drop between the input and the output. And therefore in the output you would have battery-0,7 V (a diode drop). 

Therefore in your particular circuit you would need to use Option A.







simulate this circuit &ndash; Schematic created using CircuitLab