The oscillator circuit - using discrete components - is sensitive to changes in the supply voltage. Ideally we want to use a lithium battery for a large part of its discharge behavior. Capacity is typically given for a discharge down to 2V (e.g. 235mAh for a CR2032).

To maintain a constant oscillation frequency, let's use a low-dropout regulator with an ultra low quiescent current. Texas Instrument's TPS7A02 seems unbeatable in that regard: 25nA.

An output voltage of 1.8V was chosen, as this is a common voltage for low-power digital circuits, and supported by low-power logic families such as AUP or LVC.