I suppose you know by now there has to be a problem. I have a 2kg FE on 60ltrs and the last one went for 9 months ( keeping it in the green with solenoid ! So as others say 240ltrs 3 months, sounds about right. You must have a leak somewhere, no re-filler would bother short-changing you on the quantity of the re-fill.
I recon to loose that amount in 2 weeks you should be able to hear the gas escaping. If you can't dunk the whole lot under water, try this:
1) Get a long tube (2-3 foot of 50mm plumbing pipe or the cardboard core of some gift wrapping paper). 3ft is good for this exercise.
2) Switch off all equipment (filter, air-pump?, powerhead, television, radio, fridge, anything that makes a noise in the vicinity) and just leave the Co2 running.
3) Place one end of the tube to your ear and follow the tubing flow from the FE as far as you can to the water.
It's amazing how sensitive the ear is under these conditions. It's a process I've had to use on large machinery when I've experienced loss of pressure and I'm looking for a leak.