What features cause mechano sensory adaptation?
At the molecular level this is called receptor desensitization. This is the reason why for example spices (like red hot chili paper) taste more pungent the first time you put them in your mouth and less and less subsequent times (in this case the receptor is called TRPV1).

Mechanosensory perception is mediated, at least in part, by similar transient receptor potential (TRP) channels therefore mechanosensory perception is also subjected to desensitization at the molecular level. In this particular case it is specifically called homologous desensitization.

This is, in my opinion, the primarily reason why a constant stimulus will stop producing action potentials, in essence the receptor will be desensitized and does not provoke a membrane-potential change that mediates the transmission of a neuronal signal.



Footnote

Desensitization in TRP channels happens because those channels open to let $Ca^{2+}$ ions to enter the cell and after prolongated stimulation the intracellular $Ca^{2+}$ concentration will reach the same $Ca^{2+}$ level of the extracellular medium preventing more $Ca^{2+}$ ions to enter the cell.

$Ca^{2+}$ influx into the cell is what provokes a difference in membrane-potential (i.e. the cell is now electrically charged) which mediates a signal that is then transmitted to the neuronal circuitry.