What could prevent all the sugar that is added to a glass of water from dissolving?
If the water in the glass is already saturated with sugar (i.e. it contains an amount of sugar equal to that amount of sugar that would be in equilibrium with undissolved solute), addition of further quantities of sugar will not dissolve. Of course, sugar has a prodigious solubility in water, and will form supersaturated solutions fairly easily.
Please note that saturation is an equilibrium condition, and tends to be understood less well than it might be.