How to stop the "Reopen Asset Editor" notification from disappearing in UE5.1?

Functionality has always been there.
Go to Editor Preferences and search for Asset. CHange the setting to whatever you want. Keep in mind, if you set it to always reopen and one of your assets gets corrupted, it’s really hard to get the engine running again. I recommend you set it to Always Prompt for safety. It should stay open for a while if you don’t click somewhere else first (Ie click on the content browser before you tell it to open). I just make sure I always click on open as soon as I restart.