How to avoid incorrect ADC readings due to a draining battery supply?
What you want to do is restore a DC component to an AC signal, that can be done like this: 



Here's the link if you want to play around, which I strongly advice you to do. 

And if you want to boost a signal, then don't bother, there's usually a VREF pin on your board that you can lower which effectively boosts the signal you're trying to measure. 

If Vref is 5 volt and you measure 2.5 volt and got 10 bit resolution, then you'll read 512. 

If Vref is 2.5 volt and you measure 2.5 volt and got 10 bit resolution, then you'll read 1024. 

If Vref is 1 volt and you measure 2.5 volt and got 10 bit resolution, then you'll read 1024. 

If Vref is 5 volt and you measure -2.5 volt and got 10 bit resolution, then you'll read 0. 

And if you want to reduce then voltage divide with 2 resistors. 

If you however want the Voltage Peak to Peak value, then apply a diode and then a capacitor in parallel with a resistor, the resistor will help make the capacitor bleed out. Otherwise you'll only get the maximum value ever reached which will slooooowly bleed out because of real life parasitic resistances.
That looks like this:



Here's the link for the picture above.

And here's what you probably want, with filters n stuff. 


If this ain't what you need, then write something in the comment to this post and I'll update the post.