Does the Soundbridge need a particularly strong signal or is there some kind of setting change I might make?
Firefly communicates with the SoundBridge via multicasts/unicasts. It seems that your wireless repeater does not repeat multicasts/unicasts.
Most wireless repeaters do have an option to specifically forward multicasts/unicasts. Check the configuration of your repeater.
Other than that, there is really no special network requirement. I am using a wireless repeater myself and the soundbridge is working fine.