Cannot keep android service alive after app is closed

Here is an example of foreground service that I use and that works, it remains active when the app is closed. Of course, it also must be started, and for that task the app must be running at a first glance, or a receiver of a boot event must be set, but this is another story.

public class MyService extends Service {
static final int NOTIFICATION_ID = 543;

public static boolean isServiceRunning = false;

@Override
public void onCreate() {
    super.onCreate();
    startServiceWithNotification();
}

@Override
public int onStartCommand(Intent intent, int flags, int startId) {
    if (intent != null && intent.getAction().equals(C.ACTION_START_SERVICE)) {
        startServiceWithNotification();
    }
    else stopMyService();
    return START_STICKY;
}

// In case the service is deleted or crashes some how
@Override
public void onDestroy() {
    isServiceRunning = false;
    super.onDestroy();
}

@Override
public IBinder onBind(Intent intent) {
    // Used only in case of bound services.
    return null;
}


void startServiceWithNotification() {
    if (isServiceRunning) return;
    isServiceRunning = true;

    Intent notificationIntent = new Intent(getApplicationContext(), MyActivity.class);
    notificationIntent.setAction(C.ACTION_MAIN);  // A string containing the action name
    notificationIntent.setFlags(Intent.FLAG_ACTIVITY_NEW_TASK | Intent.FLAG_ACTIVITY_CLEAR_TASK);
    PendingIntent contentPendingIntent = PendingIntent.getActivity(this, 0, notificationIntent, 0);

    Bitmap icon = BitmapFactory.decodeResource(getResources(), R.drawable.my_icon);

    Notification notification = new NotificationCompat.Builder(this)
            .setContentTitle(getResources().getString(R.string.app_name))
            .setTicker(getResources().getString(R.string.app_name))
            .setContentText(getResources().getString(R.string.my_string))
            .setSmallIcon(R.drawable.my_icon)
            .setLargeIcon(Bitmap.createScaledBitmap(icon, 128, 128, false))
            .setContentIntent(contentPendingIntent)
            .setOngoing(true)
//                .setDeleteIntent(contentPendingIntent)  // if needed
            .build();
    notification.flags = notification.flags | Notification.FLAG_NO_CLEAR;     // NO_CLEAR makes the notification stay when the user performs a "delete all" command
    startForeground(NOTIFICATION_ID, notification);
}

void stopMyService() {
    stopForeground(true);
    stopSelf();
    isServiceRunning = false;
}
}

Then I run it with

    Intent startIntent = new Intent(getApplicationContext(), MyService.class);
    startIntent.setAction(C.ACTION_START_SERVICE);
    startService(startIntent);

Please note the two constants used as Actions, these are Strings that must start with the package name.