I'm running GPSD 3.23.1 built from source but this also occurred on GPSD 3.22-4 from the debian/raspbian repositories.
When I launch any gpsd client, gpsd sends the first fix it managed to acquire, and then sends nothing else. Two fixes for this are running
ubxtool -p RESET or unplugging, then replugging the gps mouse, however neither of these persist past a restart of the daemon.
The GPS mouse is not broken as it works just fine on other devices running gpsd and on gpsmon.
The only other case of this that I could find online is on this reddit thread.