The damper suspension model in CarMaker is only meant to model the actual damping forces that are caused by the velocity of the damper. As mentioned in the Reference Manual chapter 11.3.1 "Damper", the calculated damper force has to fulfill the equation F_Damp(v_Damp=0) = 0. This is important to ensure physical stability for the model. As you can see on the figures in this chapter, the damper force acts in the opposite direction of the damper motion. Therefore, not crossing the origin point (F_Damp != 0 for v_Damp=0) tend to keep the system always in motion.

Good news: CarMaker offers an interface called "Suspension External Forces". With this interface it is possible to add additional forces for all suspension elements like spring, buffer and damper. It is well described in the Reference Manual chapter 11.1 "External Suspension Forces". In addition, CarMaker provides several examples for the External Forces Interface on c code level and for Simulink:
MySuspEF_Damper.c (< CarMakerInstallDir >/Templates/Car_Extras/src/ExtraModels)
BodyCtrl_RTW.mdl (Simulink Coder RTW Examples)