The simple answer is one extraction per portafilter filling. So depending on whether you use the smaller one-shot or larger double-shot insert, you get one or two shots per button press and after that, the grounds are considered spent.
If you’d try to leave the grounds and push the button again and again, you wouldn’t just get increasingly weaker brews, but you would notice a lot of unpleasant flavors, from excessive bitterness to sour notes. It may seem wasteful, but that’s how espresso works - you pretty much get the best of each load in one go and that’s it.
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Anecdotally, I know of a somewhat strange habit in a few Swiss households that will keep once-used Nespresso capsules (which can count as “a serving of espresso grounds”) and will use it once again for a purposely weak brew that goes into making „Kafi Fertig“ („finished coffee“), a concoction that gets spiked with a generous amount of „Träsch“ (a fruit brandy) and sugar. But that’s not a practical option for a spent coffee pickpuck which can and probably will fall apart, not to mention the food safety issues if you tried to keep it for a while. I very much don’t recommend it.