You should contact the app developer and see what they suggest.
From BBC iPlayer website.
Android Downloads – Playback issues
We’re aware of a couple of issues affecting Android 4 KitKat users in regards to playing programmes.
1. Video remaining as a black screen but with audio continuing. This is affecting all versions of Android 4.4.
If you get a frozen or black screen, you can usually fix it by pressing the back button to the programme information page, then tapping play again.
2. Playback starts to degrade after about 15 minutes of continuous normal playback of a downloaded programme. This issue is specific to Android version 4.4.3.
We’re working with Google to fix these bugs. Please be sure to accept future upgrades to your BBC iPlayer app and Android firmware so any fixes can take effect.