A1 is a voltage sense circuit with an open drain FET output. It is basically a switch that is turned on (OUT to GND) when the voltage drops to 2.4 Vdc or less.
When the voltage drops to 2.4 Vdc (or less), R1 is switched to common via A1. This turns on Q1, which turns on Q2, which turns on the LED.
When Q1 is on, C2 is being charged. The charge circuit is V+, Q1 (emitter to base), C2, R2, Q2, and common.
When C2 charges enough, it will cause Q1 to turn off, which will turn off Q2, which will turn off the LED.
Note that when Q2 turns off, the difference between two Q2 voltages, both from collector to emitter (VSAT and VCUTOFF), will be coupled across C2, further cutting off Q1. (Without this Q1 would turn right back on after a slight discharge of C2.)
C2 will now discharge. The discharge path (traced backwards) is common, A1 FET switch, R1, C2, R2, R4, and V+. Now for a discharge circuit, we need to get back to common, which from V+ is through the battery. The battery is aiding the discharge of C2. Once C2 discharges enough, Q1 will turn back on and the process will repeat.