The wax of the candle is made up of hydrogen and carbon. When hydrogen burns with oxygen it produces water, the net result is that oxygen gas is taken out of the atmosphere and turned into liquid. However, when the carbon burns, it turns into carbon dioxide - for every molecule of oxygen gas used a molecule of carbon dioxide gas is produced. Overall, two thirds of the oxygen gas ends up as carbon dioxide gas, and one third ends up as water. In theory, one of the properties of carbon dioxide itself should compensate.
Carbon dioxide is very soluble in water, much more so than oxygen.
When the candle burns, the resulting carbon dioxide will dissolve in the water at the bottom and will be removed from the air inside the jar. However, from my observations, the water rises far quicker than carbon dioxide can dissolve in water. To further complicate things, once the oxygen starts getting scarce carbon monoxide will be produced instead of carbon dioxide. For every one molecule of oxygen gas, two molecules of carbon monoxide gas is produced. Also, even when the candle does go out there will be still a little oxygen left in the jar.