Good catch. It does seem strange, especially when you consider that the same pro mini in the earlier sketch (reply #28) had a falling voltage.
As a cross-check, I plugged a different pro mini into the same usb-to-ttl adapter as used by the Moteino, and it also demonstrates a rising voltage when running the most recent sketch. So, I don't know why these Pro Mini's are behaving differently in that respect, when running the latest version of the sketch.
Changing the subject, here's some food for thought: if on the Moteino I add a 330uSec delay before starting the regular sampling loop (but still having launched the extended conversion as before at the start of the setup() function), then over several trial runs the ADC appears to nail the final bandgap voltage on its first try every time:
0. raw relative bandgap voltage=346 Elapsed time=0uS
1. raw relative bandgap voltage=346 Elapsed time=116uS deltaT=116uS
2. raw relative bandgap voltage=346 Elapsed time=228uS deltaT=112uS
3. raw relative bandgap voltage=346 Elapsed time=340uS deltaT=112uS
4. raw relative bandgap voltage=346 Elapsed time=452uS deltaT=112uS
5. raw relative bandgap voltage=346 Elapsed time=564uS deltaT=112uS
6. raw relative bandgap voltage=346 Elapsed time=676uS deltaT=112uS
7. raw relative bandgap voltage=346 Elapsed time=788uS deltaT=112uS
8. raw relative bandgap voltage=346 Elapsed time=900uS deltaT=112uS
9. raw relative bandgap voltage=346 Elapsed time=1012uS deltaT=112uS
That leads me to wonder whether running the multiple samples without any pause at the beginning, as before, is of any benefit, or worse yet, may actually slow down the sampling capacitor from reaching its final settled voltage level.
[Edit: I don't know that 330uSec is the magic number that would work on all Moteino's in all conditions, but perhaps it is, or perhaps there is a more conservative number like, say, 400uSec, that is such a magic number, and where you come out ahead (at least on average) by using it. I really don't know, as I just now stumbled across this.]