HomePods may be more reliable if they only have one network to choose from. Some dual band routers have 4 wireless channels, 2.4GHz and 5GHz, with or without client isolation. You may find things are more reliable if you only have one non-isolated network available, or at least only one that your HomePod setup device knows about so it can only pass over the one set of settings. You may also find it helps to assign an address reservation for each of your Apple devices.
I suggest you tweak your network for one channel and/or forget unneeded wireless settings in the iOS device, reset using Reset HomePod - Apple Support, and then set up once more.