In the latest version of Android, you'll find a battery saver feature called Doze. This feature allows devices that are not in use (screen off, not charging, not moving) to suspend apps so they use less power.
Suspended apps are cut off from network access, so your device will perform a periodic sync, called the maintenance window, to check for alerts. Developers can classify certain alerts as high priority so you see them more often, but they are restricted to a 15-minute interval. However, if you're not getting alerts from a particular app, or you want to see them more frequently, you'll need to add the app to the Doze whitelist. Here's how:
Head to Settings > Battery, then open the overflow menu in the top right corner and choose Battery optimization.
Toggle Not optimized to All apps. Find the app you want to whitelist, tap it and then choose Don't optimize.
Keep in mind: The more apps you exempt from Dozing, the less overall battery life you'll have, so only exempt your most important ones.
Check out CNET's guide to Android 6.0 Marshmallow for more information on the newest features.