ADS1115 interfacing issue
I asked which micro controller you are using but a mod decided (without notification) to delete the question, sad as it is entirely relevant to your question. Many micro controllers have A/D so using an I2C device would not be needed, hence lowering the cost of the cct.

From the data sheet
 The ADS111x operate in either continuous-conversion mode or single-shot mode.
The devices are automatically powered down after one conversion in single-shot mode; therefore, power consumption is significantly reduced during idle  periods
Leaving it connected is not a problem as it was designed to be left connected. Power it off the battery as during shut down current is minimal.