PC 767,
No, not if they are demoted. There have been examples of where qualified Captains have been 'forced' from LHS short haul to RHS long haul. In that case they will retain their command pay. Generally that scenario is used when there is a fleet draw down and not enough places on another fleet. Last used when LGW sent some 737 skippers to LHR but no places were available at the time on the 'Bus. They went to RHS 744 for a bit.
There can be many reasons for downgrading, not all of them based upon poor performance. Medical, age and personal wishes are all reasons for the move.