Android System Power Management

Starting with Android 5.0, many devices will act aggressively to try and save system battery power. Unless certain steps are taken, Tasker may not function as expected, either because Android is not sending it the needed signals in order to save power or because Android is even killing Tasker.

A commonly noticed symptom is that profiles with Time contexts don't activate or deactivate at the expected time.

Tasker Run In Foreground Preference

Make sure that Menu / Prefs / Monitor / General / Run In Foreground is checked.

Tasker Reliable Alarms Preference (Android 5.0+)

In Menu / Prefs / Monitor / General / Use Reliable Alarms, make sure When Off or Always is selected.

If Never is selected, Android may group alarms together so they go off too late. On some devices, Android may even kill Tasker at times if Never is selected.

Android Battery Optimization Setting

If you have reliability problems, Tasker might need to be whitelisted so that it is not battery-optimized by Android.
Vanilla Android Devices (Android 6.0+)
The location of the setting may vary per device, but a common method is to launch the Android Settings app, select Apps, click the cog icon top-right, then Battery optimization. Click All apps, then Tasker, then Don't optimize.

On a rooted device, it may be possible to change the battery optimiation parameters depending on the functionality you need from Tasker. An example app for this purpose is Naptime.

Samsung (Android 5.1.1+)
Some Samsung devices have a Smart Manager app. Launch the app, press the battery quarter of the screen, under App optimisation press DETAIL where you can adjust the settings for each app. It's advisable to disable this for Tasker if you are having reliablity problems.
Launch Settings app, select Additional settings -> Battery & performance -> Manage apps battery usage -> OFF