This has been annoying me for ages now. Homesharing not working and the circle stopping half way round. Thankfully I've found a fix after weeks of trawling the web for possible causes.
Shut down iTunes and Music on your device. Then go to System Preferences>Network on your Mac.
Click Wifi on left hand side of the window then click the Advanced button. Choose TCP/IP at top, then click Renew DHCP Lease.
When the IPv4 etc numbers have refreshed click OK and close System Preferences.
The Homesharing should now work.
The only problem is every time you shut down your Mac Homesharing will not be working again when you next try and you will have to do the above again.
Hopefully Apple will actually do something to remedy this rather than just ignoring thousands of complaints. In the meantime hope the above works for you as well as it has done for me.