Without either of those two actually busting out a tapemeasurer in that episode we're never going to know if Kido was out of Neji's range or not.

But darth, and I might be wrong here, assuming Neji can only focus on a spot 20 feet wide (6 meters) past 50 meters away.
If Kido gets past 50 feet away, and Neji doesn't initially know what direction he went, Kido's distance from Neji is enough to not get cought in his All-Around Vision.
What's more (still assuming Neji doesn't know where to look for Kido) the circumference of the circle that Neji has to scan to find Kido is 157 meters (515 feet)
That mean's Neji has to do about 26 long distance Byakugan scans (even more if Kido is farther away than 50 meters)

But, once Neji KNOWS Kido is aiming for his blind spot.... well then unless Kido is really fast (he is a ninja with many arms, traveling through forest is probably easy) then Neji's search distance (after dodging/cringing) will only have a 50/50 chance of finding Kido (assuming Kido moves from his sniping spot, which he'd be a fool not to do). If Neji scans to the right of the sniper point, but Kido moved in the other direction, he won't catch him (hence the 50/50). All of the success in this method depends on if Neji can do a Long Distance Byakugan search faster than Kido can run a distance of 20 feet. If Kido can move faster than Neji can scan, Neji won't be able to see where he is.

Here's where Neji can (and should, if he's any good) win the fight. Kido is going for his blind spot. All Neji has to do is dodge twice, facing the direction the arrow came from each time. Between the first arrow and the second is the time it'll take for Kido to move to the spot, set up and fire. And Neji should also know by now that Kido is aiming from his blind spot. Neji takes 5-10 seconds off the time he projects for Kido's travel and he can rush Kido while the guy is readying his attack.

They should really teach these ninjas some math (although my analysis depends on alot of unsure numbers, most just suggested by people in this thread.) Neji, however, should know how far, how wide and how fast he can search an area though.