要保持WiFi Direct连接在Android应用程序被关闭时保持打开状态，可以使用Service来实现。

首先，在AndroidManifest.xml文件中添加以下权限：

然后，创建一个继承自Service的类，例如WifiDirectService：

public class WifiDirectService extends Service {
    private static final String TAG = "WifiDirectService";
    private WifiP2pManager mManager;
    private WifiP2pManager.Channel mChannel;
    private WifiDirectBroadcastReceiver mReceiver;
    private IntentFilter mIntentFilter;

    @Override
    public void onCreate() {
        super.onCreate();
        // 初始化WifiP2pManager和WifiP2pManager.Channel
        mManager = (WifiP2pManager) getSystemService(Context.WIFI_P2P_SERVICE);
        mChannel = mManager.initialize(this, getMainLooper(), null);
        
        // 初始化BroadcastReceiver和IntentFilter
        mReceiver = new WifiDirectBroadcastReceiver();
        mIntentFilter = new IntentFilter();
        mIntentFilter.addAction(WifiP2pManager.WIFI_P2P_STATE_CHANGED_ACTION);
        mIntentFilter.addAction(WifiP2pManager.WIFI_P2P_PEERS_CHANGED_ACTION);
        mIntentFilter.addAction(WifiP2pManager.WIFI_P2P_CONNECTION_CHANGED_ACTION);
        mIntentFilter.addAction(WifiP2pManager.WIFI_P2P_THIS_DEVICE_CHANGED_ACTION);
    }

    @Override
    public int onStartCommand(Intent intent, int flags, int startId) {
        // 注册BroadcastReceiver
        registerReceiver(mReceiver, mIntentFilter);
        return START_STICKY;
    }

    @Override
    public void onDestroy() {
        super.onDestroy();
        // 解除注册BroadcastReceiver
        unregisterReceiver(mReceiver);
    }

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

    public class WifiDirectBroadcastReceiver extends BroadcastReceiver {
        @Override
        public void onReceive(Context context, Intent intent) {
            String action = intent.getAction();
            if (action != null) {
                switch (action) {
                    case WifiP2pManager.WIFI_P2P_STATE_CHANGED_ACTION:
                        // WiFi Direct状态改变
                        int state = intent.getIntExtra(WifiP2pManager.EXTRA_WIFI_STATE, -1);
                        if (state == WifiP2pManager.WIFI_P2P_STATE_ENABLED) {
                            Log.d(TAG, "WiFi Direct已启用");
                        } else {
                            Log.d(TAG, "WiFi Direct已禁用");
                        }
                        break;
                    case WifiP2pManager.WIFI_P2P_PEERS_CHANGED_ACTION:
                        // WiFi Direct可用对等点列表改变
                        // 更新可用对等点列表
                        break;
                    case WifiP2pManager.WIFI_P2P_CONNECTION_CHANGED_ACTION:
                        // WiFi Direct连接状态改变
                        NetworkInfo networkInfo = intent.getParcelableExtra(WifiP2pManager.EXTRA_NETWORK_INFO);
                        if (networkInfo != null && networkInfo.isConnected()) {
                            // 连接成功
                            Log.d(TAG, "已连接到WiFi Direct设备");
                        } else {
                            // 连接断开
                            Log.d(TAG, "已断开WiFi Direct连接");
                        }
                        break;
                    case WifiP2pManager.WIFI_P2P_THIS_DEVICE_CHANGED_ACTION:
                        // 当前设备的WiFi Direct信息改变
                        // 更新当前设备的信息
                        break;
                }
            }
        }
    }
}

最后，在你的应用程序的MainActivity或其他地方启动和停止WifiDirectService：

public class MainActivity extends AppCompatActivity {
    private Intent mServiceIntent;
    
    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);
        
        // 启动WifiDirectService
        mServiceIntent = new Intent(this, WifiDirectService.class);
        startService(mServiceIntent);
    }
    
    @Override
    protected void onDestroy() {
        super.onDestroy();
        
        // 停止WifiDirectService
        stopService(mServiceIntent);
    }
}

这样，即使你的应用程序被关闭，WifiDirectService仍然在后台运行，保持WiFi Direct连接的打开状态。