Several different factors will determine how long that you should be able to store mixed salt water. Pure "salt water" If there actually was such a thing. should be relatively stable for a very long time.
The issue is first and formost how pure is the water you are mixing it with and what "contaminants" are present in the salt mix itself. If you are not using RO/DI Water that is testing near zero I would not attempt to keep it long.
The mixing container is next in order as to how "stable" a material that the container is made from. Plastic Containers that are labeled as "food grade" usually do not break down as often and will not leach contaminants. The Rubbermaid Brute Containers are apparently used quite extensivly in this hobby as well as by many LFS. They appear to hold up well without "leaching" many contaminants. If it is not a food grade container or something that has been tested for leaching I would not leave it long without testing.
Cautions: Do not use any of the contaimers made from recycled materials they will definatly leach and some contain heavy metal compounds that are used in the recycling process.
One other item is exposure to the sun or UV radiation, even flourescent lights. Many plastics "including those cheap clear rubbermaid containers will "break down relatively quickly when exposed. Keep light away from your mixed water.
Good container, really pure water and a good salt mix, Kept out of the light, and re-mixed and tested before using if you have any doubts.
I personally would not mix more than I would use in a month or so at one time. I would not want the chance of something contaminating the water, I have way too many knot headed kids around my house!!!!