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NeoGAF's Physical Games Advocate Extraordinaire
Players have reported their frames per second count fluctuating and gameplay stuttering on console, even on PS5 Pro. In fact, oddly, particularly on the more powerful PS5 Pro.
Some players think this might be the result of Borderlands 4 suffering from a memory leak, although that remains unconfirmed for now. It seems restarting the game does help (some players are recommending restarting every few hours, which isn't ideal), but it's hard to say exactly why because reloading can trigger changes that would perhaps improve performance anyway, such as time of day lighting.
What we do know is that Gearbox is looking into the issue. In a tweet, Gearbox development chief Randy Pitchford told one disgruntled PS5 Pro user that quitting the game and restarting is a workaround until the developer sorts the problem out properly.
"Known issue of perf dropping on PS5 pro after several hours of continuous play," he said. "Workaround until we patch: Quit game and restart. Sorry for the friction!"
More at the link:

Borderlands 4 Performance Gets Worse the Longer You Play on Console, Randy Pitchford Suggests Quitting the Game and Restarting as a Workaround - IGN
Borderlands 4 performance gets worse the longer you play on console. Gearbox chief Randy Pitchford has suggested quitting the game and restarting as a workaround.