Does Sonos use Tunein as well or is it streaming via another source?
I wonder if the fact they drop out at different times is linked to the lack of streaming synchrony? Dot in one room, Echo in another, one a little (sometimes quite a lot) ahead of the other.
I suppose if it's to do with a third party mediator between the BBC and Tunein, that's where complaints should be directed. These devices haven't been available in the UK for long so there's bound to be some bedding in. In the meantime, might be worth trying some of Echo's other little tricks to keep your wife on board. Audio books maybe? Or just asking it daft questions to see what comes back. Mine just heard something on the TV and announced, 'I don't have any money on me'! It sounded like it thought it was being held to ransom!