How does voltage progress during discharge of a battery?
Battery discharge curves and you

Batteries indeed vary in voltage as they are discharged.  This is a function of the chemistry of the battery, and specified by the battery maker as a discharge curve, characteristic of the chemistry of the battery but also varying with the discharge rate and a few other parameters (such as temperature).

For instance, a 12V sealed-lead-acid battery's discharge curve is shown below (this is one of the most common types of small-ish 12V batteries):



As you can see, the battery starts off at around 13V and discharges to 9V before not having much life left in it.  The good news, though, is that power amplifier ICs like yours don't care much as they are designed to work over a range of voltages; for instance, your TDA7492P can run on anywhere from 8V (a single, rather flat, 12V lead-acid battery) to 26V (almost enough to run on 2 12V lead-acids in series).  The volume may go down as the battery drains, but that's OK.

I want more runtime!

You can connect batteries in series to boost the voltage (a 9V alkaline battery is really 6 1.5V alkalines in series, in a neat package), or in parallel to boost the available current capacity without changing the voltage.  Since the TDA7492P can't quite take 2 12V lead-acids in series (especially during charging), you'll have to connect your 12V batteries in parallel.  (This does introduce complications when you go to charge them, but lead-acid batteries are tolerant of this.  Lithium-ions, on the other hand...)