When Home Sharing disconnects, do the other streaming services still work? (Youtube/Vimeo etc?). In my case, when Home Sharing drops, all networking stops.
I went through many 'fixes' (changing router, turning off DHCP, switching Wifi channel to ensure it's unique in my building) with only little improvement. The only thing that made a substantial improvement was switching from Wifi to Ethernet, but even then upgrading the iOS firmware made it unreliable again.
I eventually swapped my ATV (under warranty) and it's been far better since. I do have some errors, but I never get the issue where the ATV drops the network connection completely. Fingers crossed it stays this way.