Are axons capable of endocytosis?
Short answer
In hippocampal neurons, endocytosis does occur in the axon, but only at the synapse and at varicosities.

Background
In cultured rat hippocampal neurons, Parton et al. (1992) showed that the cell body and dendritic regions are indeed capable of endyctosis. They used horse-radish peroxidase dissolved in an internalization medium. In the axon, endocytosis was only found to occur in the pre-synaptic region and in varicosities. Varicosities are points of synaptic release from the axon, outside the synapse proper.

Hence, axonal endocytosis is limited to regions where neurotransmitters are released. Presynaptic terminals often engage actively in neurotransmitter reuptake mechanisms to recycle released neurotransmitters.   

Reference
- Parton et al., J Cell Biol (1992); 119(1): 123–37