+1 for filling the bottle up near the top (leaving some room for expansion and floccuated yeast). The process taking place inside the bottle is anaerobic, that is, without oxygen. A by product of the reaction is acid, so the less water, the more the pH is going to drop over the same amount of time. This eventually is what kills the yeast (not the lack of oxygen).
A couple of things that worked well when I was using a DIY system:
1. Add an 1/8 of a tsp of baking soda. This neutralizes some of the acid as it is formed, allowing the mix to last longer. I tracked all my mixes on a spreadsheet (I am a nerd) with different recipes and found the baking soda mixes lasted a few days longer than the non-soda mixes.
2. Get a bigger bottle. The bigger the bottle, the more solution, the less acid, the longer it will last.
3. Consider ordering some champagne yeast over the internet. It is only slightly more expensive than buying bakers yeast in the grocery store, and it lasts longer. The strain of yeast is produced to be resistant to acid, since sitting up in a wine bottle is pretty similar to our DIY reactors.
4. I think the biggest success in DIY CO2 generation comes from "activating" the yeast before you seal it in the bottle. My best/strongest/longest lasting mixes came when I put the yeast in a lukewarm cup of sugar water (85-105dF) and let it be for 10-20 minutes. Then I dumped it in with the rest of the sugar, water, and baking soda and sealed it up.
I have hard of the sterilization thing, but I never did it, and my reactors ran fine.