I was having this problem also. I did all the steps suggested and I still could not send e-mails from one of my accounts. I found an article online that suggested the following for IOS 7 so I tried it on IOS 8 and it worked. Good luck!
Users must go into their iPhone settings, access the “Mail, Contacts and Calendars” settings, click on the effected account, access that account’s settings, click on the “Outgoing Mail / SMTP Settings” and, in the first activated SMTP server (the first one that says “on” to the right, retype their password in the password field.
Users must also make sure that their full email address is listed in the username field.
Even if there is already a password in the password field, users must retype their password.
For whatever reason, after updating to iOS 7, many email accounts retain the correct password for receiving emails but the correct password does not transfer over to the outgoing mail settings. Once the user reenters his or her password in the outgoing mail settings, they should be able to send emails from the iPhone, iPad or iPod Touch without any problems!