You can develope a cronic cough from PNd, but there are many more reasons for it. I am living a nighmare that started with pnd. I know have extremely heavy mucus build up and still don't have a diagnosis. Naturally, I am thinking the worst. Don't let it go on without answers. The anxiety alone can be unbearable. Get your dad to a ent and stay with it.
The first thing you need to do is a search on "laryngopharyngeal reflux" (LPR), which causes chronic cough as a primary symptom. This is a subtype of acid reflux, which involves the both the upper and lower esophogeal spinchters malfunctioning. A small amount of acid refluxes upwards into the esophogous (just like heartburn, only not enough to cause heartburn) burn continues going up higher due to the faulty upper esophogeal spinchter and splashes (I say splash, but it's more like an upward trickle) the larynx. The larynx has no natural protection against acid, and it's acid of a Ph2, super strong hydrochloric acid. The chronic cough is your Dad's attempt to clear the acid off the larynx.
How to tell the difference between LPR and lung problems? Well, can he breathe? I mean, even if he is coughing all the time, is it more of a dry cough and can he still take deep breaths? If so, it's likely LPR, and not a lung condition.
It's treatable with 2 daily doses of a Proton pump inhibitor (PPI). It won't cure it, but it will reduce the acid in his stomach enough to stop the upward trickle of acid.
For a true diagnosis, just visit an ENT and has "to be scoped", in which the ENT will observe the larynx with a mini-video camera on a wire (done in office). If there is redness and swelling of the larynx, he has LPR.
Remember, most ENTs are not that familiar with LPR outside the big cities where the professional vocalists are treated for this all the time, so you might need to tell him what the standard pharma treatment protocol is. It's 2 doses a day of a PPI, not the 1 dose that heartburn patients get.
Here's a list of the PPIs, from best for LPR to worst for LPR. Start at the top, and give each one 2 weeks until you find the one that works best for you. Most people will respond to the top two:
There is also Prilosec OTC (over the counter). I'll save you the trouble - it doesn't work for LPR at all. It works great for people with a little bit of heartburn on a regular basis, but it totally fails people with LPR, which is harder to treat and requires a much larger dosage of the medication. You can't even quadruple the OTC stuff - it's very strange.
My father had a chronic cough for years (about 4 or 5) leading up to heart surgery (one of his valves needed to be replaced). I later read somewhere (forget where, sorry) that chronic coughs are one possible symptom of heart problems.
Of course, they can be other things, too, as already mentioned. Also, something simple like a food allergy.