What determines how soon one action potential can follow another?

It is through biopsychological feedback.

A class of chemical called a neurotransmitter is important in the transmission of nerve impulses. Neurotransmitters are packaged by the cell into small, membrane-bound sacs called vesicles. Upon receiving a chemical signal, the vesicles move toward the cell membrane and fuse with it, releasing the enclosed neurotransmitters from the terminal end of the nerve cell.