Battery cutoff circuit with NE555
I can see a few problems with this circuit.

The first one is about the 7805 voltage regulator.In order to get a stable +5V output,the input voltage has to be at least 7,5V.As a battery is discharged,its outputted voltage drops:



You stated that the circuit  is to protect against over-discharge,which means to disconnect when the battery is empty. At some point,the \$V_{in}\$ will become too small for the 7805 to  work properly.In other words,the circuit may cut off the power earlier and in an unwanted way,the battery still being able to supply power.You can't really know how is a regulator going to behave if you don't run it within its operating conditions(which can be found in the datasheet).From this point of view,the design is unreliable.

Let's suppose the 7805 supplies the 555 with what's needed as intended and exactly when needed,the relay is turned off.You stated that the timer IC will still continue to draw current(this current is called quiescent current):a minimum of 3mA and a maximum of 6mA.The battery will over-discharge like this.

I believe you should choose another circuit.