Air tag not connecting to iPhone

Have been using a new air tag (Apple product) for over a year with my iPhone 12. It recently disappeared from my Find My device list. Thought might be dead battery. Replaced battery. Paired with iPhone - but will not connect with Find My again. During pairing process got message to name the device - did that. Got message to choose an emoji for it - did that. Got message warning about illegal use, then message saying "Connect", clicked on that button, then messages disappeared. Assumed all is good. Opened Find My - no air tag in list. Used option to add Device - selected air tag - got message to bring tag close to iPhone - did that but it just goes on and on trying to connect - gave up after 5 minutes. Have repeated this process 3 times. What am I missing?