For starters, tell us what series.
Is it happening to all NOW Entertainment content or just this particular TV show?
If the message is showing for all NOW Entertainment content, then have you tried clicking on the gear wheel icon (top right) of the NOW App home screen page and under My account sign out of the App.
Then power down the playback device for a minute or two, then power back up the device and sign back into the NOW App.
If that doesn't work maybe try a fresh NOW App download on your playback devices and sign back in again.
Once you downloaded the fresh NOW App and you are greeted with a QR scan code, click ok or enter on it to remove from screen, then click on the gear wheel icon to sign in with your existing NOW account details.
Also go into your NOW online account and double check your bank card details are correct and up to date.
Might seem like a silly point... but Death In Paradise is a BBC show, and all seasons (more than NOW have) are available for free on BBC iPlayer.
Although this doesnt address your problem I know.... you can still watch all that show elsewhere.