You've probably heard that your skin's pH eventually returns to normal after cleansing. That's true. But it takes its sweet time to do so—more than 90 minutes, sometimes. In the meantime, your skin will be overly oily or overly dry.
And that's just the short-term effects. Studies show that washing your face with a high-pH cleanser regularly (and you do wash your face every day, don't you?) has a cumulative effect and increases the time your skin takes to recover.
You may have noticed this firsthand, especially in winter. The more you wash your hands (or face, for that matter), the drier they get. The same goes for your skin. That tight feeling you get after washing is a tell-tale sign that your acid mantle is compromised.
This may also be why the rest of your skincare routine isn't working anymore. If you're using hyaluronic acid serums, hydrators, etc., and your dry skin isn't getting any better, chances are your cleansing habits have badly disrupted your acid mantle. Until you fix that, your skin will never go back to normal.