Although my stereo pair of HomePod minis work reliably on my own home WiFi setup, I've seen enough reports of issues out here to suggest they're a bit touchy with WiFi connections. Clearly they're not too far from your router :-).
If your router maintains separate SSIDs for 2.4 and 5.0Hz LANs, try deleting one from your iPhone/Apple ID (where the HomePod learns about WiFi connections). Alternatively, you may be able to configure your router to keep the HomePods on one band or the other, perhaps with persistent IP addresses. If you can find the time to do so, I also suggest contacting Apple Support in the hope that your call will be escalated to someone who really knows their chops and can sort it out (and they'll have another logged reason to address the apparent product issue(s).