Where I store my coach, I have AC power available, so I let it set two weeks with the unit powered, and two weeks with it not powered, repeating that cycle.
While a battery will self-discharge over time, it should retain enough charge in 3 weeks to be able to start the engine. Three months, maybe not, but 3 weeks, yes it should start.
If you are not getting 3 weeks of storage life out of the batteries, it is possible that you have some residual loads on your battery that is discharging it, even though you have the switch in the STORE position. As well, the STORE switch only affects the coach battery, not the engine battery.
For example, some owners have experienced engine battery discharge due to the radio or a light being on, even when the ignition is off.
Also, it is natural for a standard deep cycle (house) battery to lose water over time, which is the primary reason they are not maintenance free. However, if the battery is boiling off water at a high rate, say within a few days after filling, I would suspect the charger is not going into float mode (trickle charge).
A high rate of charge on a fully charged battery can cause it to overheat and boil away water. Going into float mode prevents this, so you may have a faulty combiner/charger that is not doing this.
There are really a lot of possibilities of what can be wrong, and the best thing you can do, if you feel you have the ability, is to buy a clamp ammeter, such as my favorite; the B&K Precision 316.
It can measure low-current DC, as low as 1mA, and the idea is to clamp the ammeter to each positive battery lead when you have everything off and see if you see any current flow. The nice thing about the clamp meters is you don't have to disconnect anything.
The B&K 316 is a bit pricey though, and you can buy less expensive clamp ammeters. But make sure they can read DC voltages and currents; many can only read AC. And get the lowest resolution one you can find as many cannot detect very small currents.
By using such a meter, you can see if you have any loads that are discharging the batteries when everything is off. Unfortunately though, especially if you have a faulty combiner/charger, the extreme discharge and overcharge cycles on your batteries can damage them. So in that regard, the cost of the B&K 316 is less than buying new batteries.
Even if you take the coach to a dealer to fix, having such a clamp meter will tell you immediately whether or not they did their job by finding the source of any residual loads when the switch is in the STORE position. You can put it on the battery cables before you leave the dealership and show the technician the result, and know if they found the problem or not.
The only thing that works on a RV is the owner...