I just restored to 10.2.1, and it's a lot more stable and less stutter-y than 10.3B7. A clean update to 10.3 should be better.
Just like to update to people about my problem of vanishing notifications:
1.) I had installed 10.2.1 as new using DFU mode (without backup restore), and then reproduced the issue. The problem remained.
2.) I installed 10.3 Beta 1 through 7 as new using DFU mode (without backup restore) in each case, and then again reproduced the issue for each installation. The problem remained in every installation.
3.) The vanishing of mail notifications from Notification Centre upon opening of Mail App (while no notifications or individual new or old mail is touched or opened), does not happen if the Clear button at the top right of the Notification Centre is not clicked and ALL notifications are not removed atleast once. Hence, the vanishing of notifications cannot be called an expected behaviour. This further implies that clicking the "Clear" Button at the top right of the Notification Centre is the cause of the flawed and erratic behaviour.
4.) Once the vanishing of notifications from Notification Centre has started, the vanishing act repeats even if "Reset All Settings" is done. The vanishing of mail notifications upon opening Mail App (without opening any new mail), stops only if the iPhone is reset as new using iTunes. But the behaviour again starts occurring if atleast once the Clear button is clicked and ALL notifications are removed.
5.) For argument sake, if we assume that opening and closing the Mail App (while no mail or notification is opened or even touched) is designed to clear all previous mail notifications from Notification Centre, then it is a completely flawed design. This prevents the user from viewing the new mail notifications even if he has not read the new mail, which it is not expected and desired.
6.) This current erratic behaviour is forcing the user not to click clear button for removing older notifications, as that would prevent subsequent newer notifications from appearing. This is also not desirable.
7.) The erratic behaviour of vanishing notifications starts occurring after every fresh installation of iOS (even if without backup restore) if after the fresh installation, the Clear button is clicked atleast once and ALL notifications are removed from the Notification Centre.