Well, never mind. I was disassembling the yoyo and it was screwed down tightly so I really torqued down on the halves, gripping the rings in the process. That snapped the errant ring back into place, and now all is well. To answer GrindDude's questions, I didn't get it from YYE but it was sealed in the original box in that condition.
The rings shouldn't be coming loose so easily, we would be happy to take a look at it for you.
A loose ring is usually fixable, but if it isn't then we would likely replace the yo-yo for you. Feel free to send us an email or call and we can help you out.