Hello ghiblienjoyer,
To help us get a better understanding of the issue, we’d like to ask a few questions.
1. What exactly happens when you try to play downloaded music without Wi-Fi? Do you receive an error?
2. If you get an error, what does the exact error say?
3. Does this happen with all downloaded content, or only certain songs or albums?
The above details will help us plan how to proceed.
Please also check out the information in this link, to ensure the correct process is being used to download music to play offline, so we can make sure there's no issue there: Add and download music from Apple Music
How to add music from Apple Music on your iPhone, iPad, or Android
1. Open the Apple Music app.
2. Touch and hold a song, album, or playlist that you want to add to your library.
3. Tap Add to Library.
Thanks!