This the first time I've heard of this, but I may suffer from it as well. I get it on the weekends when I do my long run. It usually hits me a few hours after the run. I don't take any medication for it. I just let it go away on its own. It doesn't happen after ever single long run though. I need to start keeping track of when it happens.
I don't know if its the same thing or not. But my nose runs like a facet whenever I run or ride a bike. Otherwise totally dry. I've just have gotten used to the snot flowing. As soon as I stop its pretty much done.
I'm wondering too if it has to do with humidity? I ran a 10K race last weekend and it was dry. I pushed hard during the race and had a few sniffles, but that was it. I'm running another 10K race tomorrow and it's supposed to be foggy and cooler. If my nose starts running, then that might be the key... Long mileage and humidity. Maybe...
I think I finally, partially pinned this down for myself. Definitely higher humidity environment, coupled with a long run. Allergens/pollution particles in the air seem to contribute to it. For the run last weekend, I noticed that while I wasn't sneezing or had a runny nose afterwards, I definitely had a major case of the postnasal drip. My next set of races aren't until the end of the month, so I'll get a better gauge then since those will be half marathons.