TinySC is configured to use the device's name as the "libraryname". 

Renamed fab4 to "Squeezebox Touch3", which triggered setting libraryname to the same value. This lead the device to no longer connect to its own TinySC instance. Looking at its configuration files I found the following:

/etc/squeezeplay/userpath/settings/SlimDiscovery.lua:
settings = {
	playerId="00:04:20:22:01:0c",
	serverUuid="73ef8617-43a0-4071-85ed-4cadd11acd2d",
	currentPlayer="00:04:20:22:01:0c",
	serverInit={ip="192.168.0.2",},
	squeezeNetwork=false,
	playerInit={name="Squeezebox Touch",model="fab4",},
	serverName="Squeezebox Touch",
}

/etc/squeezeplay/userpath/settings/Playback.lua: 
settings = {
	enableAudio=1,
	squeezeNetwork=false,
	serverUuid="73ef8617-43a0-4071-85ed-4cadd11acd2d",
	powerState="on",
	volume=93,
	serverInit={ip="192.168.0.2",},
	serverName="Squeezebox Touch",
	playerInit={name="Squeezebox Touch3",model="fab4",},
	captureVolume=40,
}

serverName in both cases still is the old value, playerInit.name isn't the same for both...

I haven't been able to easily reproduce this. It happened after I switche back and forth between different servers. But it never happened when changing a full SBS' libraryname value.