I find that I can get a 700x23 tyre pumped up twice with one 16grm CO2 cartridge and hard enough to ride. Don't know how, but I tried it a couple of months ago when I punctured, gave it as much as I could till it stopped inflating, carried on riding, and punctured again a few miles down the road, so rather than fit a new cartridge, I thought I would use up what was left in the cartridge still fitted and I was surprised to find it pumped it up hard enough to carry on riding.
Then I got a third puncture, but it was only a slow one, so I finished off the cartridge which got my tyre half inflated and pumped the tyre up hard with the hand pump, and after that I had to stop about every 10 miles to hand pump it up again before it got to soft and stayed on top of it and not allowed it to deflate too much.
The CO2 pump I have is the Giant one.
As for my tyre's going down or soft after inflating with CO2, I have never had that problem, unless it has anything to do with the what the innertube is made from.