It depends. 
If the barbs get stuck and the bee eviscerates itself leaving the venom sac behind, yes, it is always fatal. If the sting just scratches the surface and the venom sac isn’t attached, the bee will usually live. Bees tend to die when they sting mammals, because of our thick skin catching the barbs. However, if they sting other insects, which have a relatively thin layer of chitin (instead of skin), they may live perfectly healthy lives afterwards.