Persistent cough is often as a result of left sided heart failure.
In left sided heart failure, there is a problem with either the contraction or relaxation of the heart.
And so, instead of blood to be pumped into the aorta, which carries blood to different parts of the body, it regurgitates (goes back).
And blood is regurgitated back into to the pulmonary vein.
The pulmonary vein comes from the lung.
So when there is regurgitation, the blood goes back into the lungs, irritating it and causing cough.

Do you understand?