I too have this problem and have posted on a similar thread ("Mail notification not working"). I only found this thread last night as I too am desperate to solve the problem.
-I have tried all the solutions suggested here and elsewhere and none are a permanent fix, as others have noted "the problem returns within a day or so".
My setup may be a bit different, but the main issue of the native iOS mail app not fetching new mail unless manually refreshed is common to us all.
For me, I'm using Gmail and have resorted to installing and using the Gmail App together with the iOS Mail App (I prefer the UI of that over Gmail, but this issue has forced me to use both).
-By using both apps, Gmail will display notifications on the Lock Screen along with banner notifications, however the iOS Mail app will only do that randomly and then only for a day or so (then it stops fetching like everyone has said).
-What is really weird is that after I "clear" a Gmail notification from the Lock Screen, that same notification will "reappear" again at random intervals - and there are times when literally all the new mail I received within the last 24 hours will start showing up again, one after another - forcing me to clear them again or unlock my phone.
-I've tried all sorts of combinations of "notification" settings and none provide the fix we are looking for. I agree with all that it is a real problem when you depend upon being able to be notified of a new email. Without me using the Gmail app, I'm sunk trying to rely soley on Apple's Mail App.
-What's worse for me is that after forcing the "Mail" app to launch, then I get duplicate notifications from both that app and the Gmail app, and again both will randomly "re-display cleared notifications" - which forces me to re-read them to check if one is indeed "new". I'm running iOs 15.5 on an iPhone 8. Along with everyone else, I sure hope Apple will fix this, or someone will stumble upon a solution. I too am glad "I'm not alone".