After several months of less than satisfactory 'fizz' from our Gemini drinks maker and a few attempts at fixing it, I've finally worked out what was wrong. The central spike that injects CO2 into the water had come a little loose. Not enough to notice, but enough to let gas escape and preventing it from getting enough pressure to dissolve in the water. Tightened it up and it now fizzes and farts properly.
It's worth documenting!