It all depends on the device, and how it was originally set up. I've seen manually provisioned sets, where caller Id was inadvertently put into a field. That field was overriding any and all caller ID that was added by 3CX. It's rare but can happen. If your provider rejects what you are sending, on that call, they might remove it completely. I'm not saying that is what is happening, but it could be.
Obviously if all of the other sets are working as expected, then it must be something to do with the one particular extension settings, or the set.
Can you easily provision another device with the same extension number, and test that? If the issue persists then I would concentrate on the extension settings within 3CX, all else being equal (all extensions, routing outbound calls, the same way).