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Are you trying to use AirDrop between a Mac and an iDevice (e.g. iPad) ?

If that's the case, then it won't work since Mac AirDrop is not compatible with iDevice AirDrop.
 
I'm having inconsistency with AirDrop in Mavericks too, sometimes I will see the computer but then it would keep disappearing and reappearing and if I tried to send a file, the other computer would never receive a prompt. With Mountain Lion, it was flawless.
 
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