At what point is blood pressure so low that regular anti hypertensive med should not be taken?

Meds. Dizziness associated with a low blood pressure defines the level that would be too low for the individual patient on anti-hypertensive therapy.
Hypertension. If you have high blood pressure "hypertension" you will always need meds to control. If your blood pressure gets too low - which means it gives you undesirable side effects such as fatigue/drowsiness- your physician will decrease the medicine dose. Our treatment goal is a blood pressure below 120/80. Hypertension is a condition. When controlled, it will not result in complications such as stroke.