THIS! Did this finally make my Google password permanently stored on my iPhone? My Feedly app has a Google Plus share button but the iPhone never remembers my password unless I have an open page in Safari on G+. Once closed, when sharing from Feedly, I'd have to re-enter. There's no way to directly add passwords in iPhone settings, but this way may work.
How to fix Gmail incorrect password/user name error on iPhone? | The iPhone FAQ
Here are instructions on how to fix this problem should it occur on your device: 1. Quit all mail clients that are accessing the affected Gmail account. This means the Mail app on the iPhone and any other place you are accessing your Gmail from such as a computer.