Good question Ann, i thought the same thing and couldn't really find anything online about this apart from making sure the containers you are using are 'food grade' clean of dirt, air tight when closed and kept out of direct sunlight. Also don't store it near chemicals or anything else that could leak into it. I have had RO water that's 2 - 3 months old and after a topoff the tank has been absolutely fine for the shrimp.
You can buy smaller containers, you don't have to buy big 25litre drums, most shops will let you fill up a large soda bottle sized container with RO water which should last you months for topoffs.
i know i didn't answer the question, being water it doesn't really have a 'use by date' but id probably only keep the water for 3 months before pouring it away and refilling it with fresh RO.