What type of NOW Sports Membership is it, Day, Month or Mobile?
What playback devices have you tried?
What happens if you try a new NOW App download and sign back into the App by clicking on the gear wheel icon top right of App main screen.
What you describe is consistent with you not being signed in on the app.
Scroll right to the bottom of the Now display on the app, and you should find ‘My Account’ there. Check that you are logged in there with the same account details that work when you log in online.