I have been discussing this issue on the Firefly forum as well in the hope that someone there may be able to assist. Ron (the firefly expert) has recently posted the following information, which I wanted to share with you in case it prompts any settings or fixes from anyone here.
Likewise, having connected to a music library, if I stop Firefly or close itunes, the Soundbridge still thinks they are there and lets me choose them and then says "Connection to server failed". This means that regardless of if the library is active or not, the Soundbridge is not interacting with it through the Belkin, except when I do a restart.
Discovery works via multicast dns.
When firefly (or itunes) starts, it sends pre-caching announcements to the other mdns servers on the network via multicast. These will look like udp packets from the device to 18.104.22.168 port 5353.
Once it's up, it doesn't spam those anymore. Instead it waits for mdns queries (which again look like udp 5353 to 22.214.171.124) from the device asking for servers that have a specific service. The server should respond, and everything is okay.
It looks to me like something isn't right with multicast on your setup. Like multicast is only going one-way across the link.
You can try double-checking all your devices and seeing if they have an option to enable IGMP or multicast, or maybe even something about media streaming.
Failing that, I don't know a way to *make* the devices work with multicast (other than a round of firmware updates, potentially).
Thanks for your comments Mark, I am resisting the temptation to go buy more kit until I can identify the problem, as there is no guarantee that a new router or a new extender will solve the problem. So I am still trying to exhaust the settings issues. While buying a Belkin router may make for better compatability, I have had so much trouble with the extender that it has put me off buying Belkin products. I guess you are right that the best option is a more powerful router, but admit I never know what to look for in what indicates the signal strength of a router - any advice?