If you select "Do not allow" [許可しない] for background activities in the initial setup of the au Email app, the following issues may occur.
In that case, the issue can be solved by setting the au Email app to "Do not optimize battery" [電池を最適化しない] in the app's advanced settings.
Please see below for detailed steps.
Tap on "Settings" [設定] from the list of apps.
Tap on "Apps and Notifications" [アプリと通知].
Tap on "au Email" [auメール].
Tap on "Advanced Settings" [詳細設定].
Tap on "Battery" [電池].
Tap on "Battery optimization" [電池の最適化].
Tap on "Non-optimized apps" [最適化していないアプリ] at the top of the screen.
Tap on "All Apps" [すべてのアプリ].
Tap on "au Email" [auメール].
Select "Do not optimize" [最適化しない] and tap on "Complete" [完了].
If "Non-optimized App" [最適化していないアプリ] is displayed under "au Email" [auメール] the process is complete.
Please check if the issue of "Reception Failure" [受信失敗] notifications in au Email has been solved.
Has your problem been solved?