Mat,
I have exactly the same - Sonos in one room and Dot in other, both streaming same station. Sonos is bullet proof, Dot often drops out and on some days it gets to the stage where you get 1 second sound then 10 seconds delay before repeating.
Before anyone suggests it is a problem with 2 devices streaming the same feed, both behave exactly the same as above regardless of whether the other is in use or not.
I just put it down to a poor implementation of the streaming solution by Amazon, but I'd love to be proved wrong.