Using Gmail as an Android app is nothing more than using a mail client. There shouldn't be much room for error. But what if Gmail not receiving emails on Android? In that situation, the first thing you should do is check for updates before proceeding with any more drastic measures. Gmail uses Google's servers to deliver new emails to your inbox. There will be no new emails if the server goes down, though this doesn't happen very often, and it's unlikely that the server goes down for an extended time. Usually, if a server outage is the cause of the problem, you will start receiving emails again after Google has repaired it.

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Google Account recovery page