If you are only putting the Soundbridge to/from standby (ie rather than physical power off/on), then it is even more mystifying.
Hopefully one of the Roku* people - who actually know what they are talking about in this respect - will chime in here, but it appears to me that not very much happens (from a network point-of-view) when the Soundbridge goes to/from standby, ie it is "online" on the network - renewing DHCP address, broadcasting itself via Bonjour and UPNP AV, web server/config screens available to a client PC - all the time, regardless of whether it is in standby or fully-on mode.
What I was thinking, but now obviously not the case, was that on a physical power-on of the Soundbridge when (1) it has to get associated/authenticated with the wireless LAN then (2) it has to DHCP, perhaps some threading or CPU performance issue in the DGL4300 router was being hit to cause the interruption to the multicast stream you are seeing. Just going from standby to on on the Soundbridge doesn't seem to cause either of these two network actions (as far as I know) so that can't be it
When you turn the Soundbridge from standby to on, what is it doing immediately upon that switch? Is it auto-restarting an Internet Radio stream it was streaming when it was put into standby? Does it make any difference on the subsequent switch to fully-on mode when you turn it to standby when it is playing nothing vs when you turn it to standby from playing a stream?
I don't have any external multicast streams I can try with but I have a Slingbox which streams video on my internal LAN at 1-2Mbps. If you like I can try having that streaming (ie from the Slingbox to one of the PCs or Macs in the house) while I turn the Soundbridge to/from standby. Not sure it is going to replicate what you are seeing though, but I'll give it a go.
It might be worth looking in the DSLReports url=http://www.dslreports.com/forum/dlink]DLink forum[[/url] to see if there is anything posted there about multicast streams getting clobbered on a DGL4300 when some other Wireless LAN-connected device does something (whatever we manage to work out a Soundbridge does when it goes from standby to on).
Perhaps on the DGL4300 you could try twizzling the "Gamefuel" settings to see if that makes any difference to the situation? Turn it on if it is off, or off it is in, toggle the packet dynamic fragmentation switch the other way from what it is now, maybe even set up a rule to de-prioritise traffic to/from the Soundbridge relative to the default for your network? FWIW (as far as I can remember off-hand) I have Gamefuel enabled and dynamic packet fragmentation enabled, but no specific priority rules set up.