Hi Teeaitch,
Thanks for posting. Email is definitely important! It sounds like you're having some issues after re-adding an account. We'd like to learn more about what's happening to see how we can offer assistance.
For clarification, are you referring to the length of time that a mail notification stays onscreen, or something else?
If you're referring to notifications and the issue is only happening with one of your accounts, try tapping Settings > Mail > Notifications. Then, tap the account in question. Which "Alerts" do you have selected? Also, under "Banner Style," you might try setting it to Persistent to see if that helps: Use notifications on your iPhone, iPad, and iPod touch
Feel free to reply back here if needed.
Cheers.