Once your computer turn to the offline mode, you will not receive any e-mail and you can see the status is “Working Offline”
The solution is very simple, just click a “Work Offline” again to disable the offline mode :
Click “Send / Receive” > “Work Offline”
The following picture you can see the difference.
This is not joke, i make this post, because i never success through the telephone to teach user turn it back to online mode, because user always click the bottom text.