I recently bought a mini HomePod to pair with my HomePod. I was initially able to pair when I reset my HomePod and could transfer music between the speakers or play on both. However, after that there were pairing issues and the two would not connect.

You cannot create a stereo pair with two dissimilar devices. See Set up a HomePod stereo pair - Apple Support. You should be able to ask for the same content to play everywhere, but that isn't the same thing.

tt2

I haven't used those features often, my HomePods are usually in different places, but they have worked when I've tried. If you haven't already done so I suggest rebooting your router and power cycling the HomePods next time it happens to see if you can avoid having to reset them.

tt2