Android AlarmManager.set(…): notification never re

I'm attempting to use AlarmManager to schedule a delayed check in my app. (Specifically, N minutes after a user approaches a location, I want to check whether they're still there, and if so send them a notification.)

I've implemented this by checking to see whether they've entered the region in my location update receiver and, if they have, scheduling like so:

Intent geofenceIntent = new Intent(context, GeofenceReceiver.class)
// ...intent contents not important...
PendingIntent pi = PendingIntent.getBroadcast(context, 0, geofenceIntent, PendingIntent.FLAG_UPDATE_CURRENT);

Calendar c = Calendar.getInstance();
c.add(Calendar.SECOND, getGeofenceDelaySeconds());
AlarmManager alarmManager = (AlarmManager)context.getSystemService(Context.ALARM_SERVICE);
alarmManager.set(AlarmManager.RTC_WAKEUP, c.getTimeInMillis(), pi);
Log.v("Scheduling notification check for "+c.getTime());

When the battery level is high (say, 50%), everything works like a charm. But when it's low (say, 10%), I get location updates, they schedule the alarm seemingly-successfully, but that alarm never actually triggers!

What gives? Does Android stop sending certain types of updates when it's trying to conserve power? How can I work around this (short of actually keeping my app active for the duration of the delay, which causes obvious issues with battery life)?

It turns out that this is related to the use of the real-time clock.

Although I could not find the documentation it quotes (it's not in AlarmManager), this StackOverflow answer suggests that AlarmManager.RTC_WAKEUP alarms do not trigger if the phone is in power-saving mode. AlarmManager.ELAPSED_REALTIME_WAKEUP alarms do not seem to suffer this problem, so I was able to fix the issue by switching to:

Intent geofenceIntent = new Intent(context, GeofenceReceiver.class)
// ...intent contents not important...
PendingIntent pi = PendingIntent.getBroadcast(context, 0, geofenceIntent, PendingIntent.FLAG_UPDATE_CURRENT);

long millis = SystemClock.elapsedRealtime() + 1000 * getGeofenceDelaySeconds();
AlarmManager alarmManager = (AlarmManager)context.getSystemService(Context.ALARM_SERVICE);
alarmManager.set(AlarmManager.ELAPSED_REALTIME_WAKEUP, millis, pi);