I read about what discard is and I have to disagree. Just because it is not bubbling at the time, it does not mean that the starter has died. It's just resting. Unless you've really done something drastic with the starter, it will keep. It will keep frozen, it will keep cold, it will keep dried out into a powder. Maybe if you catch it on fire it won't keep.
Yeast is very resilient and is everywhere around us. Yeast will find sugars, even in a tired starter and start to multiply if you give it half a chance.