Analog to digital conversion with variable VCC
The ADXL377 has an output that is ratiometric to its supply voltage. Read the data sheet on page 3 and look at note 2 at the bottom of the page.

This means you are in-luck because if the output voltage goes down by 10% due to Vs dropping by 10% then 1 LSb of the conversion remains exactly equivalent to the value of acceleration implied by the device.