Water pump runs on 12 volt DC which is derived from your battery bank, or from your rig's onboard converter which converts 120 volt AC power into 12 volt DC power. Battery power should always be switched on while RV is in use if you have a battery disconnect switch, sure you can turn it off while plugged into power pedestal as 12 volt DC powered items will continue to work if your converter is functioning and properly wired to DC distribution center, although your battery bank will not recharge which is one of the primary functions of your onboard converter. From your description it sounds like something may be amiss with your converter although no voltage measurements were given.
