Hello DariaLeicu,
Welcome to Apple Support Communities!
If we understand your post correctly, the songs you download in Apple Music are being removed every day. We'll be happy to help.
Let's check your iPhone storage in Settings > General > iPhone Storage and make sure you have plenty of storage space available.
How to check the storage on your iPhone, iPad, and iPod touch
Also, if the Sync Library or Show Apple Music options get turned off in Settings > Music, this can remove downloads as well.
Let us know if you have any questions.
Thank you for using Apple Support Communities.
Take care!