"In November 2006, the U.S. Army bought an A380+ airship from American Blimp Corporation through a Systems level contract with Northrop Grumman and Booz Allen Hamilton. The airship started flight tests in late 2007, with a primary goal of carrying 2,500 lb (1,100 kg) of payload to an altitude of 15,000 ft (4,600 m) under remote control and autonomous waypoint navigation."
So it's perfectly possible for these things to typically fly a few kilometres above the ground. That is outside the range of small arms: the furthest confirmed sniper kill to date was at a range of 1,250 m.
So while it would certainly be possible for someone to shoot one of these airships down using aircraft or guided missiles, they would not be able to with small arms fire. Except during takeoff and landing, of course.
They're definitely not at risk to the odd potshot, but massed small arms/crew-served rifle fire could potentially be effective in the lower altitudes.
Also keep in mind that snipers are shooting at humans. That's a much, much harder target than a blimp.
And also don't forget the numbers I'm using suggest this is only plausible if you're firing more or less straight up, meaning the area you're ultimately targeting is where you are.