I am having the same issue, bought a ring doorbell 3 and the Chime 2nd Generation.
Just installed everything and when trying to change the chime tone get the same message as shown above!!!
Maybe I should have gone for the Nest Door Cam 
Interesting why canât they just release a new firmware globally, seems very unproductive and annoying updating firmware manually on a device by device basis for each person that calls support and has to wait for response!
After trying all the suggestions in this thread and having no luck, this is what finally worked for me on iPhoneâŚ
Pick your desired sound from the list, hit Save Changes, wait only about a second, and then force close the app. Might take a few attempts to get the force close timing right, but this worked for me twice in a row.
Good luck!
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I have the same issue, exactly and no matter which of the above steps I try, I cannot change the ringtone on my brand new Chime. It is just so amazing. I wonder where I else I could post to get some attention to this, like Wirecutter. Or iFixit or Consumer Reports. Customers have gone for over a year without a fix? Really?
For those of you who canât change your chime tone, maybe you should consider yourself lucky. Back in December I changed to âDeck the Hallsâ which worked perfectly and was enjoyable through the holidays. Afterwards I changed it to the âAntique Bellâ which, again, worked perfectly. Unfortunately it still plays âDeck the Hallsâ along with the new tone. I can change to any and all tones and it will change - just wonât quit playing Deck the Halls. Iâm starting to lose my Christmas spirit.