After you no longer need to aerate it with violent splashy stirring, gently stirring it is beneficial because it resuspends the yeast who keep trying to settle out, and it also degasses your must, which is a good thing in general.
Typically I aerate for the first 1/3 of the fermentation then it gets a swirl maybe once or twice more before it's done... ideally though you can gently stir it every day until the specific gravity stops moving... (if you still don't have a hydrometer, this would be when fermentation's done, usually when the airlock calms way down, bubbles aren't breaking the surface anymore).