If you have an Android cell or tablet that has stopped automatically receiving email, there are several places to investigate. The very first thing you should do is power down the cell / tablet, then power it back up and see if all is working. If that does not clear the issue, the steps below should start your email automatically syncing.
CONNECTIVITY & POWER SETTINGS:
Troubleshooting email sync on an Android device is the same as it is on every other device, start by turning everything off and see if syncing works. Specifically, turn OFF WiFi and turn off Power Saving.
1: In settings (swipe down from the top), press and hold POWER MANAGE > press and hold POWER SAVING MODE > ensure that RESTRICT ALL BACKGROUND DATA is turned OFF (is grey)
2: Confirm you have connectivity to the internet. Try to surf on your browser. If you can’t, connectivity is the issue.
3: In Settings (swipe down from the top) ensure SYNC is turned on
4: Press an hold SYNC, and ensure your MICROSOFT EXCHANGE ACTIVESYNC or other email account is included in the Accounts to Sync list
5: Ensure your email account is included in the ACCOUNTS list
Perhaps the sync is working but you have email NOTIFICATIONS turned off.
6: In Settings (swipe down from the top) > click on NOTI. SETTINGS > EMAIL (or whatever email app you are using)