HomePod mini music playback stops on 1 HomePod mini in multi-room group of 2 HomePod minis

I use multi-room audio to play Apple Music on 2 HomePod minis (directly from Apple Music initiated via either voice command to a HomePod or via a Home automation, not initiated from another device such as an iPhone or iPad) and I have regularly (as in very nearly every single day) had an issue where at least one HomePod mini stops playing at some point during the day. It has been extremely frustrating for years as I have found that one HomePod mini is playing and the other isn’t or even that neither HomePod mini is playing (and the music isn’t showing as paused when viewed in iOS, those HomePod minis show nothing playing and nothing queued up).

Others have posted about this kind of thing over the years but I’ve never found any useful information in any of those posts. However, I’ve found the solution to this problem for my situation, so I’ll list that here in the hope that it helps others:

My home network consists of 2 wireless routers, with one configured as a primary and the other configured as secondary, and what I have found is that the problem of audio stopping on 1 HomePod mini happens when the 2 HomePod minis. that are supposed to be playing the same audio are connected to different routers; once I forced both HomePod minis to connect to the same router (the primary router, though I don’t know that this is significant), the issue has not manifested itself again for now a week or more (and considering that, as I mentioned, the problem used to happen very nearly daily, I am confident that this represents a fix for the issue). So, if you have this issue and you have a similar network topography, try connecting your HomePods to the same router and see if that fixes it for you.

I should note a few things:

1. Not all routers allow you to choose the router on a per-client basis in a multi-router set up. In other words, there may not be a setting that will allow you to assign your HomePods to connect to the same router in your multi-router set up. I use Synology routers and they do not allow to assign the router to which clients should connect. What I did to get the HomePod minis to connect to the primary router is turn off the secondary router at which point the HomePod minis that had been connected to it connected to the primary router. However, since there is nothing forcing that HomePod mini to be connected to the primary router, it could at any point reconnect to the secondary router; in my case I don’t expect that will happen as that HomePoint mini’s position is such that it gets a strong signal from the primary router (from both routers actually, but I think it’s as strong or nearly as strong from the primary router as from the secondary router so I don’t expect it will switch routers). But if you have a situation where your HomePod switches itself back to a router other than the one you want it connected to, you’ll have to consider steps to mitigate the issue (which, other than moving something around or just giving up, would largely amount to switching to a router that allows you to assign clients to connect to a specific router, should such a router exist). I’m in a bit of that situation myself: I have 6 HomePod minis and 5 of them are connected to my primary router, but the 6th one has connected itself to the secondary router and speaking positionally, it makes sense that that HomePod mini would connect to the secondary router. The only saving grace for me is that HomePod mini is never included in multi-room audio. But if I wanted that HomePod mini to be a part of multi-room audio, I would have no way of making that happen reliably.
2. It may not be practical to connect all your HomePods to a single router. Meaning, you may have a HomePod that even if you could assign it to a specific router, it would not be practical for that HomePod to connect to that router due to the positions of those devices (in other words, they’re too far apart to connect effectively to one another). I’m not in this situation, but if I were then I would again have no way of making multi-room audio work reliably.
3. I have no idea if this is an issue limited only to HomePods used with Synology routers or not. Regardless, as I have noted, it’s a mess and Apple should fix it because, given #1 and #2 above, many people who want to use multi-room audio may be really hamstrung here with effectively no way to make it work.

As I said, I hope this helps others with this type of problem.