Our Bravia KDL-32W705c often gives a message 'insufficient bandwidth' when trying to stream a film from Amazon Prime. The TV connects via Wi-fi. ALL other services (Netflix, BBC etc) work OK without problems, so it can't be a wi-fi problem. We have found the only way to make it come back to life is by disconnecting the set from the power supply and then re-connecting. The streaming then works perfectly.  Re-starting the router has no effect. 

Our XBOX can connect and stream Amazon video without problems, so it looks like a Sony TV glitch. Software is 3004, up to date.