Sourdough discard can last for 6 months to a year and even longer as long as you store the sourdough discard properly and feed it every 7 to 10 days.
When kept in the refrigerator and fed every 7 to 10 days then the sourdough discard should last for 6 months or even longer.
You can also freeze the sourdough discard and it will last basically forever.
Yes you can freeze sourdough discard and it will still be good to use even a year or so later.
When freezing sourdough discard you can freeze it in ice cube trays and then put the ice cube trays in plastic.
Then when ready to use the sourdough discard just pull the ice cube trays out of the freezer and allow them to thaw out.
Some of the yeast and lactic acid bacteria may die during the freezing of the sourdough discard but not all of it and certainly not enough to prevent the sourdough discard from working.
It's best not to freeze the sourdough discard and instead use it pretty soon but if you need to keep the sourdough discard longer than a few weeks or so then it's best to freeze the leftover sourdough discard.