Android gmail not updating automatically
Also Read: How to Encrypt Emails on Gmail (Desktop and Android)?
This can be a potential problem even if it is in your own interest. When it senses that the battery is dying, it will begin optimizing your phone, and the apps installed therein, to make the most of the remaining battery juice.
You can’t expect yourself to check emails every now and then. The first thing that you can do to make sure you are receiving push notifications for your Gmail app is to check the app settings.
You'll have to add them as an Exchange Active Sync account.
Also make sure that your email app has the correct permissions to access your calendar and contacts.
It is also possible that your Android smartphone is restricting Gmail from using data?
Data optimization was created to help users make the most of their data plan, helping them stay within their monthly limits. Find the Gmail app and make sure that Mobile, Wi-Fi, and Background data, all three are checked.
Open Settings, click on Battery & performance and select Choose apps there.