Hi Ron,
I understand that you use iCloud Music Library to keep the music that you've imported from CDs on your iPhone. You've noticed that even after downloading the content to your device, sometimes it will disappear and you see the cloud symbol to indicate that it was removed from your iPhone. I'd like to point out a particular setting that I believe should clear this up.
If you navigate to Settings > Music, you should see a setting called "Optimize Storage" in the Downloads section. If you have this enabled, your iPhone will automatically remove music content that hasn't been played in a while to help you conserve storage space on your device. Can you confirm that this is enabled? If so, try turning it off and test for a while to see if you still notice the same behavior.
Cheers!