This is what I heard from a dealer (may not apply to your situation): In complex electronics, there’s a chip that regulates battery power. The chip is what tells your electronics to display “low battery,” “full battery,” or shut off your device. The “full discharge, full recharge” advice is to make sure the chip properly recognizes your battery, and doesn’t shut your device off when the battery is still half full.
In my experience, rechargable batteries have a certain number of uses before completely becoming useless. For laptops, for example, they are generally rated from 1000-2000 uses (3-5 years) before needing replacement, cell phones are probably less. Therefore, you can keep a battery forever if you never discharge it (which kind of defeats the point of having a battery at all, imho.) My wife’s laptop, for example, has been plugged in since the day it was opened, and the battery still reports the same usage time on battery for the past 6 years.