In iOS 9 Low Power Mode, the iOS itself prevents apps from having an idle screen for a long time. This is so in order to make a battery charge last longer.
If you run the meditation timer in Low Power Mode, the app will be put into the background after a short period of time. It will still continue to play the sounds and will notify you at the end (it will even allow you to save the meditation, if you are using logging), however the screen will be switched off at some point.
At the moment, the only options to keep the screen running during the session are to either switch off the Low Power Mode (Settings - Battery - Low Power Mode) or to plug your phone into a power source.