Yup, I've had that on and off for years. There are two possible reasons I can think of. First, your autonomic (small fiber) nerves are involved in breathing, so you can have trouble breathing with small fiber neuropathy. The other possibility is that it's from whatever is destroying your small fiber nerves. For instance, I have Sjogren's, which can mess with lungs/breathing. So in my case, I don't know whether it's the dysautonomia or the Sjogren's messing with my breathing.
Another possibility could be that your swallowing reflex isn't working properly, and you are dealing with aspiration. That might also cause coughing. Have you had a Chest CT?
I wanted to add though that AireScottie is likely to know more about your particular situation as she is dealing with something a bit more similar. I was only presenting another possible explanation for your coughing.
I actually have constant daily coughing as well, but mine is related to my severe-persistent asthma. I have hypoventilation, dyspnea, and breath holding spells related to my Dysautonomia.
Halbashes is right about the swallowing, because that's also mediated to some extent by the autonomic system. I have trouble with that sometimes, but the ongoing cough that I have is a little different. It usually starts up and continues for a couple days to a week. It's dry like yours and sounds kind of like someone with emphysema (I had an older relative who smoked). It sounds and feels like I'm going to cough up a lung, but nothing actually comes out. And, I have 100% no allergies or asthma. Does that sound like what you experience?
There is a form of neuropathy--"denervation hypersensitivity of the upper airways and esophagus"--associated with coughing (source: http://brain.oxfordjournals.org/cgi/content/abstract/128/12/2797). Another frequent problem in patients with various types of dysautonomia is gastro-esophageal reflux (GERD), which can be in addition to or in lieu of what I just mentioned as a cause of coughing associated with dysautonomia. There is ambulatory esophageal monitoring that can verify if episodes of GERD are related to the coughing episodes by seeing if they happen around the same time.
So, since you've hit a dead end with pulmonary on the coughing, you may want to consult with neurology and/or gastroenterology next. If, as hally mentioned, swallowing is a possible concern, a swallowing study may need to be performed as well to rule out aspiration before aspiration pneumonia develops.
I know it's been a few years, but how are you now? How and what are your symptoms?
I'm very interested to know if you have an answer to what is causing your cough. I now have two daughters with dysautonomia, and both with coughs. One has neurocardiogenic syncope, with a sort of a barking cough, like what I think croup sounds like. The other has hyperadrenergic POTS and has a higher pitched cough when she stands too much. It comes on in the evening. She has had asthma completely ruled out with pulmonology tests, but they can't tell her what is causing it. Very frustrating!