How to keep a CountDownTimer running even if the app is closed?

Run it in a service as such: use create a broadcast receiver in your activity and have the service send broadcasts.

package com.example.cdt;

import android.app.Service;
import android.content.Intent;
import android.os.CountDownTimer;
import android.os.IBinder;
import android.util.Log;

public class BroadcastService extends Service {

    private final static String TAG = "BroadcastService";

    public static final String COUNTDOWN_BR = "your_package_name.countdown_br";
    Intent bi = new Intent(COUNTDOWN_BR);

    CountDownTimer cdt = null;

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

            Log.i(TAG, "Starting timer...");

            cdt = new CountDownTimer(30000, 1000) {
                @Override
                public void onTick(long millisUntilFinished) {

                    Log.i(TAG, "Countdown seconds remaining: " + millisUntilFinished / 1000);
                    bi.putExtra("countdown", millisUntilFinished);
                    sendBroadcast(bi);
                }

                @Override
                public void onFinish() {
                    Log.i(TAG, "Timer finished");
                }
            };

            cdt.start();
        }

        @Override
        public void onDestroy() {

            cdt.cancel();
            Log.i(TAG, "Timer cancelled");
            super.onDestroy();
        }

        @Override
        public int onStartCommand(Intent intent, int flags, int startId) {       
            return super.onStartCommand(intent, flags, startId);
        }

        @Override
        public IBinder onBind(Intent arg0) {       
            return null;
        }
}

From the main activity:

@Override
protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    setContentView(R.layout.main);

    startService(new Intent(this, BroadcastService.class));
    Log.i(TAG, "Started service");
}

private BroadcastReceiver br = new BroadcastReceiver() {
    @Override
    public void onReceive(Context context, Intent intent) {            
        updateGUI(intent); // or whatever method used to update your GUI fields
    }
};

@Override  
public void onResume() {
    super.onResume();        
    registerReceiver(br, new IntentFilter(BroadcastService.COUNTDOWN_BR));
    Log.i(TAG, "Registered broacast receiver");
    }

@Override
public void onPause() {
    super.onPause();
    unregisterReceiver(br);
    Log.i(TAG, "Unregistered broacast receiver");
}

@Override
public void onStop() {
    try {
        unregisterReceiver(br);
    } catch (Exception e) {
        // Receiver was probably already stopped in onPause()
    }
    super.onStop();
}
@Override
public void onDestroy() {        
    stopService(new Intent(this, BroadcastService.class));
    Log.i(TAG, "Stopped service");
    super.onDestroy();
}

private void updateGUI(Intent intent) {
    if (intent.getExtras() != null) {
        long millisUntilFinished = intent.getLongExtra("countdown", 0);
        Log.i(TAG, "Countdown seconds remaining: " +  millisUntilFinished / 1000);            
    }
}

Note I got this code from How to run CountDownTimer in a Service in Android?, which I modified for my own android countDownTimer.