I just conducted a brief (and non-scientific) experiment to test this. In a 1L bottle, I added 2.5 cups of sugar and enough water to reach the shoulder of the bottle (approx. 3.5 cups?) and 1/4 tsp of yeast.
After a couple days, the CO2 generator stopped consistently producing bubbles. However, when I shake the solution, it will produce a huge amount of CO2. Obviously this is an impractical solution.
I drained about 40% of the same CO2 solution, added water to the shoulder to dilute. Then added about 1/4 tsp of yeast. The CO2 is now generating bubbles at a consistent pace, although is likely to not last as long (limited sugar).
It seems that at some point, the alcohol most certainly kills the yeast preventing further sugar digestion. I don't know if there is another reason (e.g., sugar saturation) but from what I've just experienced it does seem that too much sugar can artificially stop the CO2 process before all the sugar is digested.
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