For most apps, there is no reason to ever stop either monitoring or ranging. The main reason people think they need to do so is to conserve battery. But iOS CoreLocation and the Android Beacon Library automatically put limits on beacon scanning when apps are in the background to keep battery use in check.
Unless your app is designed to be kept running in the foreground for an extended period of time, or it takes extra measures to extend background ranging time, there is usually no reason to limit ranging. Most of my apps start both monitoring and ranging at startup and never stop.
Of course, there are use cases where you simply do not want to get beacon discovery callbacks any more, so if this applies to your app then by all means turn off ranging and Monitoring as appropriate.