I found out the hard way that sometimes when you make changes to an email account on the iPhone the settings don't stick. My experience was specifically in changing the Advanced » Authentication setting to NTLM for an Exchange account. The problem, however, may be more widespread than that. The solution was easy:

Make your desired changes to the settings in the mail account. Then go back to the account's main screen, scroll to the top, and move the Account slider to OFF. Go back to the Home screen, then go back to settings and turn the account back ON. Check that your settings have saved. That should do it; I hope this helps a lot of people avoid this pesky iPhone issue.

[robg adds: I haven't experienced this, but then again, I haven't changed my account settings and I don't access an Exchange account.]