Cut It Close,
Any unusual noises coming from that side of the system? Do you know how many hours are on the hydro belt, or is it possibly the original? It seems like the belt might be slipping but you will usually see that in the left side since it has less pulley wrap on the left hydro pulley. The slope question is related to the wheel motor, a common symptom of a failing wheel motor is it will seem fine on flat ground but the demand of the slope will make it seem like it looses all drive. Check for any loose fittings on that side of the system to make sure there is no air possibly getting into that side of the system.