Since it only happens when sending, make sure you have send
authentication enabled.
Go to Tools, Accounts, select that account, Properties, Servers.
The box for "My server requires authentication" must be checked.
If no improvement, test your password by logging in to webmail:
http://gmail.com
If that works, it proves you have the correct username and password.
A likely reason for the username/password failing is account corruption.
One thing you should try as a possible quick fix is to delete that corrupted
mail account, restart Windows Mail, then recreate that account.
If that doesn't fix it, more drastic measures will have to be taken.
Which antivirus are you running?
As a minimum, email scanning in the antivirus must be turned off,
although that may not be sufficient to eliminate all bad effects.
In a worst case scenario, your antivirus may need to be uninstalled.
If turning off the email scanning function does not resolve your problem,
consider upgrading to Windows Live Mail, because it is less prone to
suffering bad effects from overly aggressive antivirus programs.
http://download.live.com/wlmail
Email scanning in any antivirus must be disabled, for reasons
explained here:
http://thundercloud.net/infoave/tutorials/email-scanning/index.htm