+1 on indefinitely. think of it being in your fish tank without any waste being added to it. Im not sure how i feel about keeping it air tight though. I like to have a lot of air and water flow in mine to keep it aerated and mixed the best i can. Although i get very little evaporation in my basement so topping off isn't that often for me.
It depends on the conditions you keep it in. I live in az so I keep it for no more than a month in my hot garage. I would suggest a powerhead and an airstone or a Venturi style powerhead. I have mine set to mix the water every other day, just to keep things moving in there. I would cover but only if you have an airline running into it, otherwise your looking at slimy water ( at least in my heat).