A connection error when opening the PBS app on iPhone or iPad means that you are not connected to WIFI, have cellular data, but have this option turned off in your Apple Settings.
The error will appear like this on screen when you try to open the PBS app:
To fix this error, you will need to open the Apple Settings app, then scroll down through the list until you see PBS. Select PBS, then make sure the Cellular data is green.
You can then restart the PBS app and it should now load normally.