Stirring has no effect on solubility. Solubility is defined as the amount of substance that dissolves in a given amount of solvent and is determined by adding a solvent to a solute until no more solvent dissolves even with vigorous stirring. This means solubility is independent of mechanical agitation.
Factors that do affect solubility include temperature, pressure, solute-solvent interactions and the common-ion effect. The stronger the interactions between the molecules of the solute and solvent are, the higher the solubility of the solute in the solvent becomes. Many ionic solids interact strongly with polar solvents, such as water, making these ionic solids highly soluble in water. The same stands for organic solids and non-polar solvents. The general rule is that like substances prefer to dissolve in one another.
When the ionic compound is dissolved in a polar solution that already contains one of the ions that the solute dissociates into, this decreases the solubility of the ionic solid in water. This phenomenon is known as the common-ion effect and can be explained by Le Châtelier's principle, in which the net ionic dissociation and recombination equations are hindered in the forward direction because of the preexisting presence of the first ion in these equations.