I have fought with this problem for a long time now. I have seen many people suggest changes to settings thinking the problem is fixed. My impression is that the ASUS just resets when you make a change and that clears up the problem Temporarily.
I have found one workaround that fixes the problem and as long as you don't make any changes to your Asus router it should stay working. The other day i turned on QOS on my router and it broke my homesharing. When i turned it off it stayed broken. I reset the router and it stayed broken. Here is the fix i use to get my apple home share back and working.
1. I go to the wifi network that my apple devices are on. In my case i am using the 2.4Ghz becuase of some older devices.
2. I turn off all security and encryption on the wifi network setting it to "open system"
3. Reconnect my iOS devices to the open network. apple tv, phone, macbook etc.
4. Home sharing should now be again working (but you don't want to leave your wifi open).
5. Go back to your network settings and change your wifi security back to your preferred setting. I use WPA2 -personal
6. Go to your iOs devices and reconnect them to your wifi network (you will likely have to enter in the passwords again)
7. once all you devices are connected you should be all good and homesharing should work again.
A couple foot notes
a. At the time of this typing i was using the latest firmware on the asus 3.0.0.4.374.239
b. if you don't want to break your setup again DO NOT change any settings in the Asus. I find that when i change some settings (regardless of what they are) it will cause the homesharing or airplay network to collapse again.
I know the problem is not with my apple devices but with my router. I still have my old router and when i plug it in the problem never occurs. Becuase my old router is so old i needed a faster router for apple tv and bought the asus. IT was good for some time and then started causeing to drop the homesharing network. For a while i could reboot the router and it would fix the problem but one day that stopped working.
It is a pain but at least if you can get your apple home share network up and not fidget with it you can watch and listen to content when you want.
I regret buying this router and wish someone could tell me technically why this problem happens. I am in the IT industry and i can't figure it out but i think it is just buggy software.