I was very relieved to find this thread as, like others, I assumed that the problem was unique to me!
Before I found the thread I had called Apple support in the UK where I live and if they are aware of it being a latest software issue, they weren't letting on.
I explained to them that I had changed routers, switched to a hard wired ethernet connection (assuming that it was a wireless problem) and radio still cut out after 10 minutes with an error message. Support agreed that I had done everything they would have asked me to do.
With that, they sent me a packing box and asked me to return the Apple TV box, telling me that they would replace it ( I had 6 weeks left on my warranty).
During this period, I discovered this thread, but I chose not to tell Apple that I suspected that the software update was at fault as I wanted to see how they would handle it and what they would send me.
Today, a brand new Apple TV box arrived. Of course the first thing I checked was the software version.
6.0!
Maybe I'm being paranoid but I suspect this means that they know that shipping me a box with the latest software release would present the same problem so they sent me a box with the last version. Maybe not, maybe it's just old stock.
I have switched off automatic updates.
Early days, but I was able to run radio for about 25 minutes with no issue before I had to leave the house, so I'm pretty sure that it'll be fine now given the previous software release.
Happy to have radio functioning again - it's what I use my Apple TV for 99% of the time.
Thanks to all for the invaluable information on this thread. I'll keep monitoring it to find out when it's again safe to upgrade the software.