The three AAAs ran out of battery much quicker than expected, and I figured it might have something to do with the voltage divider.
Based on the fact that you used 100K resistors, the voltage divider
probably had very little effect on your battery life.
Is power constantly flowing through the voltage divider, even when I'm
not reading any data from the pin?
4.5V / (100K + 100K) = 22.5uA.
22.5uA * 4.5V = 101uW
If so, does this reduce battery life?
It does affect it, but in your specific case the effect is very small.
The capacity of a typical alkaline AAA battery is on the order of 1 Amp-Hour. With a 22.5uA load a 1 Amp-Hour battery would last..
1 Amp * 1 hour / 22.5uA = 44444 hours = 5.07 years.
Its not likely that the 200K resistors are the cause of your battery drain.
Its more likely that your micro-controller, voltage regulators, and other parts on the board are draining the battery.
You didn't mention if you are using rechargeable batteries or not, but many AAA rechargeable batteries will self-discharge in about a month with no load.
I noticed the voltage divider was very inconsistent, is there a better
way to lower the voltage going into the Arduino's analog pin
A voltage divider is a good way to lower the voltage. The reason your readings are inconsistent is because the divider has very high output impedance.
100K * 100K / (100K + 100K) = 50K
Your ADC (like most ADCs) probably has a sampling capacitor inside of it. When the ADC begins to take a sample it must charge the sampling capacitor. For an un-buffered type ADC the sampling capacitor typically charges from the load. It will take a while for the divider output to settle.
For example if the internal sampling capacitor was 20pF then the time constant would be...
20pF * 50K = 1us.
If you wanted the output to settle to 8 bits of accuracy then your acquisition time would need to be at least...
ln(2^8) * 1us = 5.5us.
If the acquisition time on the ADC is not long enough the output won't be settled and your samples will be inaccurate. You need to buffer the output somehow.
If you sample infrequently, you can just put a 0.1uF ceramic capacitor between the divider output and ground. The external capacitor will charge the sampling capacitor very quickly thus making your settling time very low and improving the sampling accuracy.
Also note that the 50K output impedance makes the divider output very susceptible to electromagnetic interference from nearby digital circuits. EMI will result in random noise in your measurements. The capacitor will help with this as well.
If your ADC has any DC input leakage current specified you may also need to add a micro-power op-amp configured as a voltage follower as a buffer.