This may happen if your network connection is temporarily disrupted or if your data connection is blocking VPN connections:
- Tap the switch to abort the connection process
- Open the Settings app and navigate to Settings > General > Reset
- Tap on Reset Network Settings
- Reboot your device; make sure your Wifi is connected
- Try connecting the app again
If this does not allow the connection, then it seems your current network is blocking the connection ports used by the iOS app. In such a case, a different VPN setup would be required. Please try one of the following recommended setups instead:
OpenVPN: https://www.privateinternetaccess.com/pages/client-support/ios-openvpn-connect
L2TP: https://www.privateinternetaccess.com/pages/client-support/ios6-l2tp