If you are concerned about having to change the battery, then a good idea would be to add a simple battery monitor to detect when the voltage drops below an acceptable level. A good IC for doing this is the ICM7665 from Dallas/Maxim. I have used it in several projects of mine, it has a very accurate trip point and will work anywhere between 1.6V and 16V (it can be pushed to 18V). It has an internal refference that it compairs to the voltage on the set pins, when the set pin voltage drops below the 1.3V refference, it's output changes states.
Here is the data sheet:
https://www.electro-tech-online.com/custompdfs/2011/10/ICL7665.pdf
The equations can be a bit confusing so I will give you a simplified version of what you need to figure out. Remember that output 1 is normaly low when the voltage is greater than 1.3V while ouput 2 is normaly high. On page 7 the example some example circuits are shown. I would not recommend using the first example because it will oscillate when the voltage is near the trip point.
The threshold detector with hysteresis is one that I have used once before but the calculations tend to give some very odd resistor values. This cirucit is better for monitoring higher voltage supplies that the IC can't be connected to. Assuming R1 and R2 are your voltage devider with R1 going to ground and R3 being the output from the hysteresis then your equation is:
For the same supply voltage;
R2= R1*([Upper voltage-1.3V]/1.3V)
R3= (R2*[lower voltage-1.3V])/(upper voltage-lower voltage)
For seperate supply voltage;
The equation for R2 is the same
R3= (R2*[Vcc-1.3])/upper voltage-lower voltage
If you are using the schematic shown in Figure 5 (this is the one that I most commonly use) then the equations are as follows:
R2= R1*([lower voltage-1.3]/1.3)
R3= R1*([upper voltage-lower voltage]/1.3)
It's that simple, hope this helps.