Sky are closing the service. If the subscrition is on a rolling monthly basis once the last month you paid for is up the app stops working as there is legally no ongoing contract. Check the date you last paid if it is over one month ago then unfortunately you can no longer use the app. From the help page I assume the last date Sky took payment was the 6th June hence why 6th July is the last date.
It would have helped if they put notices up in the app but Sky are not known for good communications they recommend using the Now TV app instead..