If you're using Windows Phone 8.1, you won't be able to use the BBC iPlayer anymore after April of this year. The app is having its support for the older Windows OS cut in order to make room for development on other platforms, and the developers encourage users to update to Windows 10 Mobile if they intend to keep using the app.
If you do upgrade to Windows 10 Mobile, you’ll be able to play content from BBC iPlayer and BBC iPlayer Radio. If you remain on Windows Phone 8.1, you’ll only be able to play radio programmes.
You'll still be able to check out radio shows if you don't update, but your access to video through the BBC iPlayer app is going to be totally cut off until you upgrade. BBC reminds you that you can see if your device is eligible to upgrade to Windows 10 Mobile through the Upgrade Advisor app.