Use Connection Doctor
Use the Mail Connection Doctor to check your Internet connection or the status of your email accounts.
Tip: When an account or network is offline, a lightening bolt icon 
or a warning icon 
is shown at the end of the Favorites bar (just below the search field) or in the Mail sidebar. You can click the icon to take an account online, if possible, or to see status information.
Choose Window > Connection Doctor.
Review the status information.
If you’re connected to the Internet, there may be a problem with the account’s mail servers or your account setup. Follow the instructions shown in the Details column. To quickly see the account in Accounts preferences in Mail, double-click the text in the Details column.
To see log information while Mail tries to connect to mail servers, click Show Detail, then click Check Again.
When you’re done, click Check Again to see if your actions resolved the problem.
If the problem persists, contact your email account provider to verify your account details and setup.
If you contact Apple Support with Mail issues, you may be asked to select the Log Connection Activity checkbox in the window. When selected, diagnostic information is collected while you use Mail, to help Apple Support understand and resolve Mail issues, investigate issues with your computer, and help improve Apple products and services. The diagnostic information collected might contain personal information, including the content of your email messages. If sent to Apple, this information is used by Apple in accordance with its privacy policy and is not shared with any other company.
To see the folder of log files in the Finder, click Show Logs in the Connection Doctor window. After you provide log files to Apple Support, deselect the checkbox to turn off connection activity logging. You may want to delete the log files, as they can be large.
Learn more about the Apple Privacy Policy at www.apple.com/privacy.