Hi taterbug77,
Thank you for using the Apple Support Communities. I see you may be running into an issue with music and I'm glad to see how I can assist.
It sounds like this is happening with music you've purchased in the iTunes Store as opposed to downloading from Apple Music or syncing with iTunes; is that correct?
Can you provide a little more detail about what's happening? Are you downloading these songs directly to your device and then find they delete at some point after? Or is something else happening?
Are you seeing a cloud icon next to the songs when you look at your library? Are you able to play them without tapping the cloud icon? If not, what happens when you try?
Which exact iOS version are you using under Settings > General > About?
Does the same thing happen on both cellular data and Wi-Fi?
To look at another possibility, if you are subscribing to Apple Music, this setting from the article titled Add music to iPhone and listen offline is worth checking out:
- Free up music storage: If iPhone is low on storage space, you can automatically remove downloaded music that you haven’t played in a while. Go to Settings > Music > Optimize Storage."
I hope this helps get you started. Kind regards.