Why is my battery losing power?

So I've recently bought a used car from a dealership. The
car is an 03' Honda Civic Si, and it has 225000 miles on it.
Everything works great, however after driving a constant
hour or so the battery light will come on. I've had several
people look at it, two auto store clerks, my original dealer,
and a mechanic. Every one of them has tested the
alternator and the battery and both check out fine. The
original auto clerk told me that if I replaced my alternator
that I would probably have the same problem. I recently
bought an FM transmitter that shows the volts of the
battery. Recently after about 60 miles of consistent driving I
noticed after my battery light came on that the voltage was
staying at a constant 12 volts. It had remained at 14 the
entire drive until all of a sudden something causes it to
drop. What is strange to me is if I go out and start it now,
the car starts and it remains at 12v as if it's being charged.
What could knock the volts down so low? Why wouldn't the
alternator charge it back up? I originally thought my AC was
doing it, but the last two times it has happened has not
been air related.