Hello Maryquestion,
Welcome to the Apple Support Communities!
I understand that your iPad is having difficulty staying connected to your network. You have already done a great job of troubleshooting by restoring your iPad back to its factory settings as well. To continue troubleshooting, I would suggest trying to isolate the network. Does this only happen on your home network, or does it happen across multiple networks. The following article may have some more helpful information in it to help you resolve this issue.
If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network - Apple Support
- If someone else set up your network, ask them for help. If you’re using a network at a company, school, hotel, store, or other free Wi-Fi location, find an employee for assistance.
- If you're connected to a Wi-Fi network but you can’t get online, try to use your Wi-Fi network on other devices. If you can’t get online using your other devices, there might be a service outage. Call your cable company or internet provider for help.
- Try connecting to a Wi-Fi network in a different location. If your device can connect, you’ll need to get help with your Wi-Fi network. If it can’t connect to any Wi-Fi networks, contact Apple.
- Update your Wi-Fi router with the latest firmware and make sure the router supports your Apple product. For more information, contact the manufacturer of your router.
Have a great day