App Login Problem (iPhone/iPad)

I am having a login problem with my iPad and iPhone on apps which require a username and password. When I enter my username and then try to enter my password, the username disappears. When I enter the password first and then try to enter my username, my password disappears.

This has been happening for at least two weeks. I can't open any apps which require username/password unless this information is already stored in the app.

I have been searching different forums and I haven't seen anyone else with this problem. So I expect the problem is just with my devices. I have rebooted the devices and reinstalled the apps. None of these actions have solved this problem.