I made a sphere which moves and which must emit liquid continuously, but the liquid flows in the first frame only. I probably forgot to check something somewhere, but where (file joined)
With your current setup, you need to put the source particles in a point group called "particles".
You can use the sop node flip dop source to more easily set up a flip source if you're using the dop workflow. Or without changing your sop setup at all, you can just use a pop source inside the dopnet rather than a volume source and it will work as is.
edit: you can also just clear the group name from the volume source dop under the particles tab