Both storing a discharged battery and overcharging a stored battery are not good. You have to decide about leaving the charger connected based on your own comfort level.
On the one hand, you want to keep the battery charged because you may need to use it and because it's not good for batteries to be stored in a discharged state.
On the other hand, you don't want to worry if you charger stays connected that it is overcharging the battery and damaging it.
My experience (a FWC-supplied house battery that's now 4 years old) is that a completely disconnected battery hardly discharges any appreciable amount over 4-6 weeks. My experience also is that at other times I've left it plugged into shore power a lot and it still seems OK. I did buy the IQ-4 accessory for the IOTA charger which is supposed to be a "smart charger", one which "maintains" the battery when fully charged at an optimum voltage.
Tips for storing a battery not connected to a charger:
First, make sure you charged the battery before you store it.
Second, be sure a stored battery isn't connected to any load, even those sneaky little loads like the carbon monoxide detector or even a voltage meter or TriMetric; all draw a minuscule amount of juice which will still drain the battery given enough time. There's probably a fuse on or right next to the battery; pull that out to make sure there's no load (and remember where you put the fuse for when you need to put it back in again).
Third, go have a home-brew and don't worry about the battery. The worst damage to a battery is caused by deep discharging it beyond 50% of its rating, not by storing a charged battery. There's nothing you can do about that when you're simply storing the battery, so don't worry about it. Relax. Plan your next trip.
