Cannot record on cd music from Apple Music I have paid for

To expand a little on what ed2345 has told you, Apple Music is a subscription service. Once you stop subscribing, you lose access to the music.

That's completely different to buying the music. If you buy the song (from the iTunes Store), then you get to keep it and burn it to CD.

Make sure you are using Purchased tracks, not Apple Music subscription tracks. The latter cannot be burned.