...In addition, 1/4 tsp. of standard-rise bread yeast is a small amount. Sugar water contains lots of energy, but almost no other nutrients needed for yeast to live. The nutrients come mainly from the yeast itself, and are recycled as older yeast die off. But I've heard there's a minimum amount of yeast that must be used for this recycling process to work, otherwise the mixture will "stall" as nutrients are too limited, and don't become available for recycling fast enough. For 1.5 cups of sugar and ~6 cups of water, I think I've gone as low as 1/2 tsp. of yeast, but usually 3/4-1 tsp.
The bottles in the thread I referred are set up for "quick burst" production, not long-term. The bottles are rotated through a daily refresh, so that each produces the initial "fizz" initially common to yeast mixtures. The heaviest production usually occurs in the first 5 - 7 days, tapering off in a pronounced slope. That leaves one each bottle always at the various stages of output and the overall quantity of gas produced at a fairly constant rate.
The problem with adding too much sugar to a long-term bottle lies not only in the lack of proper nutrients, but the produced alcohol content as well. Once the level particular to the variety of yeast is reached, production essentially stops as yeast cells die or go dormant (in combination) and all the left-over sugar simply sweetens the by-product. Alcohol, like nitrogen to fish, is a toxic waste product with the yeast.
If you want a long-term arrangement, it's best to use something other than baking yeast, and champaigne yeast is usually readily available in most areas at some of the small, DIY shops for brewing. When you refresh the bottle at the end of a production run, just carefully decant the settled bottle, leaving the dead/dormant yeast cell layer as intact as possible. Then, when the liquid is added shake well to distribute everything. In this way, and with a fair amount of caution toward cleanliness applied, you don't normally have to re-establish the colony with fresh yeast and can go through several cycles until a few other "nasties" finally make their way into the mix and it starts producing vinegar instead of alcohol...