We experienced the same issues. In the middle of November, the HomePod suddenly stopped working. No rhyme/reason or previous warning signs...just died. This Apple product gets the least amount of abuse compared to our others (ie it sits on a shelf) yet it has died to quickest!
We called Apple, they set-up a Genius Bar appt, but the day before we were gonna drop it off for a repair, the local store called and said the "service fee" is $279 USD. We laughed and told them that they got "service fee" and "cost to buy a new one" mixed up. Silly them!
Anyhow... We gave Apple another ring yesterday to see if they could throw us a bone, but the rep said the only option is a "repair" for $279. Again I clarified to him that its not a repair, that is buying a new one. He did finally confirm that indeed they do not do repairs on HomePods, they just give you a new one if you pay $279. His recommendation was to buy a new one and get AppleCare. Ooof!
I left a complaint on the homepod feedback page. In the past, for me, Apple has been stellar for standing by their products when its a QC issue...which this seems to be. I've had replacements for computers and phones given to me easy peasy. And yes I get it, sometimes you pull a short straw and you get a lemon, but the fact that they don't have any reasonable repair option for this $300 paper-weight (*cough* $350 when newly released in 2018) is simply frustrating. Maybe if enough people report a problem, there will be some resolution...but for now I guess it stays on the shelf where it always was and we won't be rushing out to buy another homepod after this experience...regular or mini.