It is your stainless steel wire ring that caused the problem. I had 4 of those and every single one of them broke within 2 or 3 trips. The breaking point is always at the end of the wire connecting to the screw connector. Basically the connector came off the wire. I only lost 1 luggage tag (and it was a cheap one), the rest of them broke while the luggage was with me.

I only got them because I thought they look cool.