I see 2 possible scenarios for the battery voltage.
- You have some accessory that is pulling a small draw consistently. 0.7v is not a huge amount, but that not very little either. So it is possible that something is drinking all night and bleeding that voltage off.
- Depending on how you're getting the 12.5v reading, that may not be where the battery is stable, i.e. the battery may not be holding all the juice needed, and may be shedding the amount it can't store. If one cell is not working properly, that could account for the loss of storage.
In my experience, once you remove a battery from a charge cycle it will gradually reduce voltage until it hits a stable point. So it's possible the 12.5v is before it has stabilized, in which case you battery could be a little weak. But it's also possible there is some parasitic drain happening. Acceptable drain would be at max 0.5mAh (from what I've found) which isn't much. So unless you have some accessory that is sucking juice all the time, I'd say it's likely (not guaranteed) something is wrong with the battery.
You should definitely check for parasitic drain to make sure (rather than jus buying stuff to throw at the problem). Make sure you do this 1 hour or more after you've stopped running the vehicle. (From what I understand some systems will continue to operate for a bit afterward, so if you check too quickly after driving you will likely get an inaccurate result.)
Final possibility (I think), if the battery is reading 12.5v while running with minimal accessories then it could be a bad/weak alternator. Generally voltage at the battery (after 10-20 min of alternator charging) should be around 14.1~14.5v. If it's more than 1-2v volts lower, then probably bad alternator function (which can be caused by a loose or deteriorated belt - may not need a new alternator) or some hefty accessory usage. If it's more than 14.5~15v while idling then there is a strong possibility the alternator is outputting too much voltage and adversely damaging the battery. In this case you'd likely need a new alternator or a rebuild because I believe the voltage regulator is usually inside the alternator for fullsize vehicles.
(Note: Vehicles that have been outfitted for high accessory loud output, whether OEM or aftermarket, may have larger alternators that output more voltage.)
As far as the practice of running it down to 11.5v, like Weather Vane said, there shouldn't be anything wrong with that as long as the process of charge/discharge is gradual.