How much driving to fully charge the 12V?

So, here's a question: in normal usage, defined next, why is the 12V measurement in ACC mode, or better yet, directly at the battery with the Prius off, ever anything but the fully charged voltage?

Let's define normal usage as unlocking the car, getting in, with the doors open only a few minutes, driving around for a while, turning the car off, getting out in a minute or two, and then locking the car. Door open uses about 500mA, but for a normal trip that is just a couple of minutes at each end, let's say 4, so 1/15th of an hour, and 0.5/15 Ah or 0.03 Ah, ie, nothing as the battery is 320CCA or around 46Ah. Whenever the car is in READY the battery will be at around 14.1V and charging at up to 4A. Unlike a normal car, the current/power needed to start the vehicle is not very large. We can estimate it from the IG-ON current draw, which is around 9A if no cabin fans are going, 21A if max fan. But it only takes seconds for the car to get into READY. Let's say 30s for an absolute worst case. 30s is 1/120 of an hour, so 9/120 Ah to 21/120 Ah = .075Ah to .175Ah. At 4A it would take 68 to 157 seconds to recharge. Granted the recharge may be somewhat less efficient than this, but back of the envelope, it seems like the battery should be maximally charged whenever the car is off. Unless of course the car is doing something to avoid charging it up all the way or there is some built in parasitic load. The normal load on the battery when the car is off, after a bit of time passes, is around 20mA. That would eventually run the battery down, but if nothing else is going on, that would take 46/.02 hours = 2300 hours = 96 days. After sitting 12 hours that is 0.24Ah, which is larger than is needed to start (see above) and works out to be about 216 seconds.

So, maybe if the car only makes very short trips it can come up negative for each day? Maybe a better way to think about it is the "sitting time" each day is 24h minus the driving time. If the car is to remain fully charged, let X be the time driven (in hours), let NS be the number of starts that day, let 0.1Ah be used at each start, and 2 *.03Ah used entering and exiting the vehicle. (This 0.16Ah per trip value seems conservative, the real value is probably lower.) Then (omitting units):

(24-X)*.02 + NS*(.16) = 4X ->
X = (.48 + NS *. 16)/4.02

NS=0 -> X = .119 h = 429 sec = 7.15 min
NS=1 -> X = .159 h = 572 sec = 9.54 min
NS=2 -> X = .199 h = 716 sec = 11.94 min
NS=3 -> X = .239 h = 860 sec = 14.34 min

If the actual time driving is more than X the car will either be maximally charged or at least be more charged than it was. If it is driven less than X the battery will be discharged by some amount. If it isn't driven at all, to make up for it, the amount X must be added into subsequent days driving to maintain the 12V level. This analysis completely ignores all the things the car does when it turns off, like pumping inverter coolant into the thermos, and it ignores any self discharge the 12V battery may have.

Anyway, this does suggest why the 12V battery has been low on our car, as we have been making a lot of short trips consisting of multiple "hops" as in the table above, and the driving times on many of those are less than the calculated X values.