As that time draws close, you'll have to turn the radio up a little
more to get the same volume, but you probably won't notice. Then, the
sound will become a little distorted, and you might eventually notice
that. Not too much later, what you describe will happen. (The FM
section takes more power than the AM and will stop working sooner.)

I've never seen a radio in which the tuner sections are separately powered.
Compared to the output stages, they draw little current.

And very few radios -- the GE P970A being an exception -- have separate AM
and FM tuners. We never established if this was the case with the
Superradio.