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I would recommend 2 articles for this, first iOS: Troubleshooting Wi-Fi networks and connections found here http://support.apple.com/kb/TS1398
- Restart your iOS device.
- Tap Settings > Wi-Fi and locate the Wi-Fi network to which you are connected. Then tap > and Forget this Network. Try to connect to your desired Wi-Fi network again.
- Note: You will need to enter your Wi-Fi password again if your desired network requires one.
- Turn your Wi-Fi router off and then on again2. If your ISP also provides cable or phone service, check with them before attempting this step to avoid interruption of service.
- Update your device to the latest version of software.
And then this section at the bottom if needed:
- If you are using a public or commercial network that requires a login or subscription, see this article for more information.
- Check to see if you have a self-assigned IP address:
- Tap Settings > Wi-Fi and locate the Wi-Fi network to which you are connected. Then tap >.
- If your IP address is 169.254.xxx.xxx, see this article.
- If you do not have a self-assigned IP address, see if other Wi-Fi devices on your network have Internet access.
- If they do not, consult with your network administrator or ISP for further assistance.
- If they do, reset network settings on your device by tapping Settings > General > Reset > Reset Network Settings.
- Note: This will reset all network settings including: previously connected Wi-Fi networks and passwords, recently used Bluetooth accessories, VPN and APN settings.
And if the device providing the 4G Wifi, then this article I would look at next if the issue persists:
iOS: Troubleshooting Personal Hotspot