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Not really sure it has a shelf life, given that you keep it agitated and aerated. I keep 10-20 gallons of water in a tub all the time, with a heater and powerhead dropped in. I only empty the tub out once every 4-6 months to clean the calcium carbonate out, so some of that water in there is 4-6 months old.
No, it can't go bad. But without a powerhead the salt may settle to bottom and even if it's covered there will be some evaporation. So when you go to use it you'll have to heat it, mix it and check specific gravity all over again so really what's the point of storing it?
if you have a reef, it's not wise to keep mixed water over a couple days, especially if you rely on the changes to add components like calcium and alk to your water. calcium starts to precipitate out after a short time.
try a test of newly mixed salt water and some that's been in the mixing barrel for a week. you'll see a big difference on the test kits.