After you’ve established a Wi-Fi Direct connection with your printer, your mobile device or computer might maintain that connection after you turn the device or computer off and on, or leave and then move within range of the connection again.
If you cannot connect to the Internet, confirm that you are connected to the name of your local wireless Internet connection in your network or wireless settings.
You may have to make your mobile device ‘forget’ your printer, and then retry connecting with the local network.