I don't know much about pastel pencils--so there could be something like a mechanical pastel pencil out there, and if so, hopefully someone will answer this question with information about such a pencil.
But, I have a hunch that they don't exist because of the different composition of the "lead" in a pastel pencil vs. that in a mechanical pencil.
I have only ever used pastel sticks, so I had to look up the details of how a pastel pencil is created. I found this description of the Caran d'Ache brand of pastel pencils on the Dick Blick website:
Caran d'Ache Pastel Pencils are made from pure raw materials to create a pastel pencil paste that is fed by hand into round moulding dies, oven-dried in special baskets, carefully glued between two strips of the finest California cedar, and cut into lengths to produce several pencils....As a final step, the pencils are sharpened in a double-cone process, a particularly delicate operation for such a fragile product
(I added the emphasis to the last line)
It sounds to me as if the ingredients that make up the "pastel pencil paste" simply don't have the structural integrity to hold together as individual sticks of lead without being enclosed inside a protective shell. Manufacturers might be able to make the pastel sticks of the appropriate shape and diameter to work inside a mechanical pencil, but those sticks might be too delicate to be transported to customers. They could also be too delicate to be able to function with the type of mechanism that advances the lead in a mechanical pencil; depending on the softness of the actual pastel lead, the compression mechanism that advances the lead in a standard mechanical pencil might actually crack/shatter/smoosh (that last is a scientific term) the pastel lead.
I know, for example, that my regular pencil sharpener does not work well to sharpen my colored pencils, which are wax based--I actually have a special sharpener designed to work with colored pencils that is MUCH more effective. My guess is that there is something similar going on with the pastel pencils that mean that they simply cannot work with the mechanisms in a mechanical pencil.