Just encountered this when I changed my Google Account password: my iPhone 4 stopped sending and recieving mail from that account even after I updated the password in Settings -> Accounts. The iPhone pops a message saying the password is incorrect. When you try to leave, iPhone tells you that you may not be able to send and recieve mail as a result.
For security purposes, Google occasionally requires you to re-enter your normal password when using their various web services. When you change your password, you may need to pass a captcha test to re-enable IMAP on your gmail. Props go to MadebyMark for the link.
Google has a pretty unassuming unlock page here you must visit with using the browser on the mobile device you’re unlocking. Pass the password and captcha test and your iPhone should be able to get google mail again. Google did not notify me that I might need to pass a captcha test after updating my account password. How was I supposed to know that updating a password might disable gmail IMAP support? The answer is buried in a Google support forum.
UPDATE: If you are using the native mail application on the iPad, you will have to do the same device unlock you performed on your iPhone. I’m interested in any information that better explains how Google authorizes the use of mobile devices. Please @jetsetter or post in the comments if you have further observations.