There seems to be a recurring issue with losing the password in Apple Mail when using Gmail (if you need instructions on how to set up Apple Mail to use Gmail click here).

Here are the instructions:

Open Apple Mail.

(1) Mail > Preferences

(2) In the ACCOUNTS window that pops up select the account in the left column that is having the issue sending messages out.

applemailaccount1(3) In the column on the right select OUTGOING MAIL SERVER (SMTP) for the account having the issue:

applemailaccount21 (4) Now click on the two little arrows on the far right of the above smtp server you select and SELECT:

Edit SMTP Server List…

In the next pop up window it should show the smtp.gmail.com server is selected:

applemailserverlist1 Be sure the radio button is selected for USE DEFAULT PORTS (25,465, 587)

Be sure the check box is selected for USE SECURE SOCKETS LAYER (SSL)

Authentication: Password
User Name: PUT YOUR EMAIL ADDRESS HERE
Password: PUT YOUR PASSWORD HERE
Type in your password in the PASSWORD field and SAVE.
Close all the windows. Now test your email by sending one out.