HomePod minis appear to have a networking bug related to Apple's Private Wi-Fi Address 'feature'. If the iPhone you used to setup the HomePod mini hasn't had that feature turned OFF for your home WiFi network, the minis periodically switch out their hardware address ad it causes a variety of issues.
On your iPhone, go to Settings --> Wi-Fi --> [Your Home(Pod) Network] > (i) > "Private Wi-Fi Address" = OFF.
NOTE: This will cause a "Privacy warning". You can ignore this. There's no risk; it's your network.
Next, reboot everything (including WiFi infrastructure) and hard reset your homepod minis to redo the setup so that they learn you've set Private Wi-Fi Address to 'OFF' for the network. Many folks report improved stability and reliable operation after doing this. This guy reports observing MAC address changes on his HomePod mini until he turned off Private WiFi Addresses and reset his homepod: https://www.reddit.com/r/HomeKit/comments/rxkcqh/homepod_mini_private_address/.
Good luck with it. Please let us know if how it goes.