Dealing with new outliers after capping
Once is all it takes; you're done. The point of dealing with outliers is that they are rare. Forcing your model to fit to those outliers can make its performance against inliers (which it will encounter far more often) worse, and that's A Bad Thing. Although you now have values that look like outliers when you plot them, this is an artifact of your earlier transformation - those values should be within the "normal" expected range of values for your data.