I love to run and I love to run in the nature. I bought a stroller for running and today it was my first (beautiful) running experience with my 8-month-old baby, but I realized that in the forest there is little bouncing because of the rough terrain. Can I harm my baby? A friend told me that it can be dangerous for his nervous system.
No, you should be fine. People think of babies as extremely delicate, and they are a bit fragile, but they aren't THAT fragile. I think some of this impression comes from "shaken baby syndrome," but people don't realize the degree of force with which those babies get shaken. A bumpy ride isn't going to damage the nervous system, or else they'd never let babies ride in cars, at all.
This is a pretty common question/concern, if Google is any indication.
I'd be more careful with a very young infant, lacking in head control. They don't recommend use of jogging strollers for babies under 6 months, in part for that reason.
A friend was running in the grass with one of these large tire three wheeled offroad looking strollers. The toddler loved this until he unexpectedly hit a bump and the toddler fell out of the stroller. Remember you are pushing from the bar on top so if the front wheels stop suddenly then you effectively push the stroller right over. The toddler was buckled in properly, but the buckles are more to keep the kid from getting out than to protect them from something like this. There were only minor scrapes, but if he hadn't landed in grass it could have been worse. If it's a smooth path with no ruts, roots, rocks, etc and you can see the ground over the top of the stroller easily then it's probably ok. If this is the sort of path you have to watch to make sure you don't trip then reconsider.