Why does enthalpy remain constant during the isenthalpic process?

Let's apply the energy balance equation between the upstream and downstream of the throttling valve.

Q + h1= W + h2 + d(KE) + d(PE)

Q = 0

Reason: There is not enough time and surface area available for heat transfer

W = 0

Reason: There is no lifting of any weight (no thermodynamic work)

d(PE) = 0

Reason: There is no potential head difference

d(KE) =~ 0

Reason: there may be an increase in velocity at the outlet compared to the inlet but in many cases the change in kinetic energy is insignificant.

Hence we remain with

h1=~h2 (kJ/Kg)