Low Power, Energy Saving, Do Not Disturb Mode

Some devices have a specific battery optimization that will stop notifications from showing.

Android - "Energy Saving" or "Battery Optimization mode". On the device, check Settings > Battery > Battery Optimization or Adaptive Battery > Find your app and press Don't optimize

ManufacturerDescription
AsusCheck your app in the Auto-start Manager.
Huawei Step 1: Settings --> Advanced Settings or Power Saving --> Battery Manager or Protected Apps --> select the app to protect it.

Step 2: Settings --> Apps or Notification Manager --> Advanced or Notify for your app --> Ignore Battery Optimizations, select the app and ignore it.

Step 3: Settings --> Notification Panel & Status Bar --> Notification Center, select the app, then activate "Allow Notifications" and also "Priority Display".

Full Instructions

Pre-EMUI 5.0 / Android 7 - Go to Settings > "Protected apps", check your app. Full Instructions
LeEco/LeTV Step 1: Settings --> Permissions --> Manage Auto Launch --> select the app to protect it.

Step 2: Settings --> Battery --> Power Saving Management --> App Protection, select the app and ignore it.
LenovoSettings --> Power Manager --> Background App Management, select the app and ignore it.
OnePlusSettings > Battery > Battery optimization > Top right 3-dot menu > Advanced optimization, turn off.

Settings > Battery > Battery optimization > Your App > select Don’t optimize.

Settings > Alert slider to make sure it’s set up the way you want.

Make sure that Gaming mode is off or go to Settings > Advanced > Gaming mode and toggle Block notifications

Look in Settings > Apps and check the Notifications settings for any problem apps.
More details
OppoSettings --> "Security settings" --> "Data saving" and enable your app.
SamsungDisable battery usage optimizations

Settings > Device Management > Battery --> Unmonitored apps > Add your app

Make sure notifications are turned on for your app

Settings > Apps > Your app > App Settings > Notifications > Set as Priority

Samsung devices with Android 8 & 9 have a “Standby” mode where the app will not get any notifications, updates, or Intents until the app is opened again by user. This is default to 3 days, but can be increased to 7 days.
SonyTap on the battery icon. Go to Power Management --> STAMINA mode --> Apps active in standby --> Add your app.
Xiaomi/
Redmi
Settings > Installed Apps > Your App > Battery Saver > change option from "Battery Saver" to "No restrictions".

Provide authorization to your app to run at startup by activating the AutoStart option in Settings > Installed Apps > Your App
OR
Security (App) --> Permissions --> Autostart - Enable your app

Settings > Notifications & status bar > Turn on "Show Notification Icons" (if you want to see icons) > App notifications > Your App > Show notifications

Settings --> Developer Options. Disable "memory optimization". To enabled Developer Options go to Settings --> About. Tap on MIUI 8 times. Full Instructions
MIUI 10Settings > Battery & performance > Choose apps > Select the app that is not showing notifications > Select No restrictions

Settings > Permissions > Autostart > Toggle slider next to the apps that are not getting push