my preference is not to store large amounts of water for any length of time. there's not really a need, and it's possible that RODI can suck up TDS from the air or the container it's in if it sits around.
i leave my unit wet. typically it gets used once a week to make enough for my weekend water change and top off.
i have it so that i have to screw the supply line on to the faucet whenever i'm making water. when i'm done, i unscrew the supply line, but otherwise leave the unit untouched.