My Homepods can't connect to the network,

Do you have the issue that your HomePod is saying "check if the HomePod is connected to the same network as your iPhone?

I had this, and me and my local Apple authorized repair center had a difficult time fixing that one. What eventually worked was this

If you can't reset HomePod mini using the Home app, or by pressing the top of HomePod mini, you can restore it. Restoring your HomePod mini resets it and updates it to the latest software.

1. Plug HomePod mini into your computer using the USB-C cable that came with it.
2. Wait a few seconds. If you're using a Mac, open a Finder window. If you're using a PC, open the latest version of iTunes.
3. Select your HomePod when it appears on your computer. 
4. Click Restore HomePod.

You'll see a notification on your Mac or PC when HomePod is done restoring.

After I did this it still didn't work, but after a week it started working again

Is there a specific error message you can share? They won't work properly on networks that are running in guest mode or with wireless isolation/security active that blocks devices from seeing each other.

tt2