Happened to me today when I got upgraded day of departure. Got a notification of a seat change but the app wouldn’t load with the new seat (and showed the “tap to check in” screen, which wouldn’t actually respond when I tried to check in). Had to go through dl.com to get a boarding pass with the correct updated seat assignment
The least-inconvenient workaround for this is to use your mobile wallet. Whether iOS (Apple Wallet) or Android (Samsung Wallet, Google Wallet, etc.), the boarding pass will properly update for schedule changes, gate changes, seat changes, boarding zone changes, etc. My Samsung Wallet-stored boarding pass even properly updates the boarding group color and number (looking at you, DL IT) when getting upgraded to a different service class.