I have the same problem. The answers below do not help.
I am posting this in the hope that a reply addressing the issue will be received.
On my Mac I can get to the below screen by going through Account - Purchases (this is one artist). They do not download or at most one song will download. In music/iTunes only song previews will play.
You can see what the OP is talking about. There are download 'buttons' but they do not work.
BTW I can play some of them on my iphone, I believe the ones I purchased on my phone are the playable ones (on the phone) - not on my Mac .
Is it because they auto downloaded on my phone when I purchased them and they can only be downloaded once? That's fine but I expect to be able to play them (not just the previews) on other devices.
At the same time I am receiving repeated offers for a month free Apple Music. It feels like carrot and stick. I already pay for a lot of iCloud space, enough to cover my purchased music, thanks.
It is not a case of number of authorisations.
It is not a case of hidden purchases.
It is not a case of cancellation, renaming or reissuing of songs or song titles.
It is not a case of path to song because it worked fine until recently.
