It was a guess, but the scenario I described is very common one. It's so common that I had about a 90% chance of nailing it. There's an old saying in the deep cycle battery world:
"Deep cycle batteries don't die, their owners kill them."
Most people do not understand deep cycle batteries. Why would they? Most only know their starter battery, and even at that, all they know is that it works, and that the alternator has something to do with making it work. You turn the key, the motor starts, and because of the alternator giving the battery a constant charge, you aren't likely to run into a problem with deep discharging, much less chronic undercharging. There's no reason to learn all that other stuff.
But with deep cycle batteries, used for house power (inverter), it's a completely different deal. I treated my first deep cycle battery the same as I treated any other battery I'd ever had. And, like most everybody else, I promptly killed it.
Since then I've learned the how's and why's of deep cycle batteries. I've also had a boat or two in my day, and with a sailboat, for example, knowledge of deep cycle batteries is critical, especially if you're out in the ocean and out of sight of land. And when you think about it, the requirements of a truck or van, and a boondocking dry camper and a boat are all about the same.
Most people don't know that their starter battery and their house battery (if they are different) usually require different voltages and amperage currents during the charging process. The alternator on this Sprinter, for example, puts out between 13.2-13.8 volts, usually around 13.4, yet AGM deep cycle batteries require 14.2-14.4 volts. So to properly charge the house batteries I'd have to use an external voltage regulator, one for the starter battery and it's 13.x volts, and one for the house batteries and their 14.x volts. Trying to charge deep cycle batteries at 13.x volts can take days, instead of hours.
The only way to keep your batteries in good shape is to use a battery monitor, like a Xantrex Battery Monitor. It monitors all amps in, and all amps out, and gives you a reading to let you know the current state of your current. hehe It will scream at you (or automatically fire up the APU) when the batteries reach 50% DoD (or whatever level you specify). It also takes into account the Peukert Effect and reports the remaining and used amps accordingly. The Peukert Effect is, uhm, well, sucking amps out of a battery is like MPG with fuel. The faster you go, the less miles you'll get out of a gallon of fuel. If you suck amps at a really high rate, like with an electric heater, air conditioner, circular saw, just like bad fuel mileage, your amp hours will decrease significantly from the battery's amp hour rating - a 300 amp hour battery bank may only yield 210 amp hours. Conversely, if you draw amps in a trickle, you can actually have more available amps than the battery's rating - a 300 amp hour battery may yield 400 amp hours.
A good battery monitor will take all the guesswork out of it. A good battery monitor is not cheap. It's, in my humble opinion, ridiculously expensive, but it will, absolutely, turn batteries that normally are lasting a year or two into batteries that can last 5-10 years. And if you have several batteries, especially expensive ones, then the battery monitor becomes cheap at twice the price.
For those that care, cheapest place I've found for the Xantrex monitor is here:
http://store.solar-electric.com/xabamosy.html
I've got the monitor, the communications kit (for connecting it to your computer, and you need to also get a Serial-to-USB adapter unless you have a serial port on your computer (most computers don't these days)), the temperature monitor, and the connections kit (for wiring it all up). All total, a cool $420.00. But, for $225 you can get just the monitor, use your own wires to connect it, and you're good to go. The temperature of a battery affects how many available amps can go into and out of the battery, and the temp sensor allows the monitor to account for that. Not that big a deal if the batteries are mounted inside, but it's an issue for batteries mounted under the hood or in a box outside. I got the communications kit 'cause I'm a computer geek, and there was simply no choice in the matter.
Your mileage may vary.
Slow and steady, even in expediting, wins the race - Aesop
Hey, he couldda said that, ya know.