To setup Evolution to remember passwords do the following:
1) Edit -> Preferences -> Account
2) Select your account and hit Edit
3) Click on Recieving Email tab
4) Check the box that says Remember password
5) Click on Sending Email
6. Check the box that says Remember password
If auto-login is setup you will be prompted for a password still when accessing your email. This is your keyring password used to login. It can be removed as follows:
1) Go click Applications > Accessories > Passwords and Encryption keys
2) The should be entries there listing an array of keyring passwords
3) Right click on them and select change password
4) Enter the old password if you have one then leave the new password blank (A warning message should appear, accept it)