Hello shiraishi,

The resource below provides some troubleshooting steps to isolate what is causing the issue with your email account.  I've highlighted some key information, but you can access the entire article by clicking on the link.

If you can’t send or receive email on your Mac

https://support.apple.com/en-gb/HT204075

Follow these steps if the Mail app in OS X suddenly doesn't send or receive email.

If your Mac is connected to the Internet, but Mail no longer sends or receives email messages, the issue could be with the provider of your email service. Or you could have missing or outdated settings in the Accounts section of Mail preferences (Mail > Preferences).

 

If Mail says that your account appears to be offline

Mail might say that your account appears to be offline due to a network problem.

If you're connected to the Internet but your account appears to be offline, your email settings might no longer be correct. To view your current settings in Mail, choose Preferences from the Mail menu, click Accounts, then select your email account.

OS X automatically uses the correct account settings for many email providers. You can use Mail Settings Lookup to view those settings, or get the settings directly from your email provider. Then compare them to the settings you see in Mail preferences. 

 

If you still can’t send or receive email

1. Make sure that you installed the latest Mac software updates, especially if the issue occured immediately after installing a previous update.
2. In OS X El Capitan, you might see a status icon and brief error message in the upper-right corner of the Mail window, beneath the Search field. The message might say “Network Offline” or “Login Failed,” for example. Click the message to see more details about the issue.
   
   
    
3. Check your connection in Mail Connection Doctor. It might be able to tell you more about the issue.

 

Take care,