You can store your sourdough tightly closed in the refrigerator. Without being fed, it will keep there until the best-before date - and sometimes longer ;-) You can leave the sourdough in the bag and close it tightly with a clamp or something similar, so that no germs or refrigerator smells get into the sourdough. Alternatively, you can transfer the sourdough from the bag into a tightly sealed container, it's entirely up to you.
Otherwise, with continuous feeding, your sourdough will theoretically keep indefinitely. As long as you take good care of it, you have a friend for life!