Sorry for being late at the party 
@Smojo already found the issue, Signal introduced a new detecion of play services/microG with version 8.11.x.
Starting with 8.13.x there is a new toggle switch in settings - data and storage: “stay connected in background”: If you use Google Cloud Messaging, you’ve probably set this to “Off.” If you want to use it with Signal’s background websocket, it should be set to “On.”
But on two FP6 devices it still doesn’t work as reliably as it did up to version 8.11.x. (Not sure if it’s related to iodeOS 7.6: Broken IPv6 support on WLAN; I’ll test it without Wi-Fi in the next few days…)