Why is the Atomic Blimp not showing up?

When you download the Atomic Blimp DLC, a blimp icon appears at the Vinewood Racetrack and a new contact is added to your phone, "Blimp". I know I can get to the Blimp by simply accessing the racetrack.

The problem is whenever I try calling the "Blimp" contact, a woman answers and says exactly this:

"I'll send one out to you right away".

No matter how long I wait, the blimp never shows up! I have tried this dozens of times in multiple areas and the blimp icon never moves.

Out of rage, I then take my anger out on nearby citizens:

Anyway, What am I doing wrong?

EDIT:

The problems addressed in this question have been fixed with the recent patch.

Solution 1:

Go the the wiki and it explains everything.

Can be ordered on a special in-game app after completing Franklin's intro mission. Has to be picked up at the location give on the map. One of the most common locations for pick up is at Los Santos International Airport.

So you have to go to that location. The woman just says she'll have it ready for you on the pad. Not come to you.

Solution 2:

You're misunderstanding something.

When you call the Blimp contact, the woman says:

Of course, sir. I'll get one sent out to the nearest available drop-off point.

The thing is, unlike a cab, that can go almost anywhere, a zeppelin is huge and can't simply land whereever.

Calling the Blimp makes its icon appear on your map. You have to go there yourself.