Station keeping for many days at a time is what border survailence is about. That precludes using non-electric fueled vehicles.
A far as being shot at by folks on the border; You would want the vehicle some distance inside the border for several reasons. First you really don't want to look straight down, you want to be looking at an angle. That way you can see much more detail about your survalence target. Second, you don't want your ship to cross over the border if something goes wrong. You want some place to bring it down on your side of the border.
Imagine how difficult a shot it would be to hit a target 3000 ft up and 1 to 5 miles horizontal distance away. Without tracers, you would have no idea how close you are to a hit.
I'm pretty sure that sensors on board would be able to tell if the vehicle was being shot at. Either acoustic sensons listening to the shockwave from a bullet or hearing the sound of a bullet hitting the envelope. If that were the case, the vehicle would start looking for the shooter, He'd have to be reasonably close. I'm sure that after a few folks were caught for shooting at the vehicle, that sort of thing would drop off in frequency. There are systems being used in Iraq that can tell the dirction a bullet comes from by acoustic triagulation.
A problem that would be made very much easier by the large size of the vehicle. By placing the acoustic sensors far apart you get much greater accuracy, and aerostats are big.
The biggest problem I see with using these things is dealing with storms. Historically, that is what destroyed most LTA ships.
