My previous response regarding Bonjour helped some but problem returned.
I discovered I could do and soft reset on my Router, which required re-entering the networks. After that, iTunes worked normally, for a while.
I also discovered, I could create a guest network on my router and that worked.
I do believe it is related to the Router or at least the internet access. Currently, I am running with IPv6 disabled since it seems to cause problems. I was getting constant reconnects on the IPv6 TCP connections.
If you don't have a good and stable internet connection, you will see problems like we are both seeing.