Unfortunately in my experience, it is completely random and there is no easy way to keep your PDI active. I've had my PDI go into hibernate after just a few hours of inactivity, other times I've had it still active the next day. I'm assuming they do it based off of need, but either way, it is completely inaccessible. Many users over the past many years have wanted more options to keep PDIs open, and not deactivate after 10 days of inactivity, but that has not happened. Further on this point, ServiceNow actually used to allow you to recover a backup of your PDI if the 10 days of inactivity elapsed, but now they no longer offer that service, and the only recommendation from them is you make your own backup of your PDI in the event 10 days of inactivity elapses.
If you're interested in backing up your PDI, here is a link to a helpful blog
Back up PDI
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