Ensure you have the most recent version of the app installed. This can be found on the Google Play Store by clicking: HERE.
Android prevents background activity to conserve battery whilst Battery Saver Mode is active.
You can also find more information from Google addressing this by clicking here.
Ensure your phone is not on Low Battery Mode/Power Saver Mode (or whitelist the app for low battery mode if available as a setting on your device).
In addition, ensure background refresh is enabled for the RADIO.COM app.