It may not be the case that suddenly people just stop emailing you, what it could be happening is that the Mail Metro style app stop syncing all your emails.
If you noticed Metro apps in Windows 8 do not have many settings or places where you can check for problems. This can make it a bit challenging when troubleshooting issues. Sure is that because most Metro apps are small in sizes, you can just reinstall the one it causes issues to see if that fixes the problem. Good thinking, but that might not work, so what could you do? For the Mail app synchronization issue you can try the following:
1 Use the Ctrl+Shift+Esc keyboard shortcut to open the Task Manager.
2 At the bottom of the window, click More details.
3 Next from the Apps list, select Mail and click End task. Important, do the same for the Live Communications Service process located in the Background processes section (refer to the above image). Then simply relaunch Mail and voila, and new emails will start flowing once again.