Before asking for a replacement of the same ring type you may wish to consider whether an Alpha ring would work better. But you really do need to try the ring with another NFC device and see if that helps at all first.
The rings, because they are different in behaviour to 'standard' tags can still fail to read on a phone that works with standard tags and yet not with the ring which can still be quite fine even if it does not read with your device. To reiterate, if you are not able to read the standard tags from a reasonable distance (around 30 to 40 mm with a good phone) and in a large area on the back of the phone then this is a good indicator that your NFC function is not behaving as it should.
This can mean a problem with your phone. If it were me, I'd check all the options and if it were my phone at fault I'd want to repair that.