I noticed that the Edge Explore (v4.10) with Battery Saving mode on quite often (4 times during the 40 minutes ride over the city) hanged (or actually did not go to sleep and did not turn the display off) with the screen saying "going to sleep in 3 seconds".
Interestingly the screen was active that time, updating the map or whatever it was displaying. Tapping the screen would bring it back to normal operation after which it went to sleep correctly.
Another observation is that when stuck in this "going to sleep in 3 seconds" mode when I stopped (alarm triggered) the beeper emitted the sound but there was no pause (double vertical orange bars) icon neither the green triangle upon ride resume. When I tapped the screen on the ride it then displayed the green triangle as if these notifications were somehow queued but not displayed.