To the best of my knowledge, the stock Android Mail app is badly broken. I could not get it to reliably fetch mail from the various email accounts I have, and it just about refused to send mail under any circumstance. I googled the problem and it is widespread. The best alternative appears to be a free mail client called K-9 Mail.

Please note that the stock Android Mail app is flatly unable to access gmail accounts (gmail is not even an option in the setup), you have to use the separate Android Gmail app for that. That Gmail app is another beast which, while working, is not very friendly either.

So I resolved to trying K-9 Mail and it seems to work. Some fiddling was required with the settings, particularly for my Cox mail account.

These are the steps I had to use to configure K-9 mail for my Droid Razr (Android 4.0.4 Ice Cream Sandwich)

1. From the Home screen, tap the K-9 Mail button.
   • If you have not previously created this account, tap the Menu button and select Add Account.
   • If you have setup this account previously on your phone, tap it, press the Menu button, then More, Settings and finally Account Settings
   • Enter your full Cox.net email Address and Password and tap Manual Setup.
2. From the Setup menu, tap Fetching Mail, and at the bottom tap Incoming Server
3. Enter the following Incoming Mail Server information in the spaces provided:
   • Username - Enter your email username (do not enter “@cox.net”)
   • Password - Enter your email account password.
   • POP server - Enter pop.east.cox.net (on the West coast, you may have to enter pop.west.cox.net)
   • Security: SSL (Always)
   • Authentication: PLAIN
   • Port - Enter 995
4. Tap Next. If the screen returns to the Fetching Mail menu, the incoming server settings were correct.
5. Click the Back key and tap Sending Mail.
6. Scroll to the bottom and tap Outgoing Server
7. Enter the following Outgoing Mail Server information in the spaces provided.
   • SMTP server - Enter smtp.east.cox.net (on the West coast, you may have to enter smtp.west.cox.net)
   • Security: SSL (Always)
   • Port: 465
   • Require sign-in: checked
   • Authentication: AUTOMATIC
   • Username: your Cox mail user name (without “@cox.net”)
   • Password: your Cox password
8. Tap Next. If you are returned to the Sending Mail menu, the configuration was good.
9. Tap the Back button until you are returned to the Account page.
10. Notes:
    • depending on where you are, you may have to turn WiFi off. Some ISPs block pop mail to servers outside the ISP's domain and I have not found a way around that.
    • The resulting problem is that it appears to me that fetching mail over 3G or 4G uses much more battery than WiFi. 3G is definitely better than 4G from a battery life standpoint.