Due to the fast response ability and high ramping rates, pumped-storage hydropower (PSH) plants are playing an increasingly critical role in mitigating power generation fluctuations induced by the growing proliferation of renewable energy resources. However, because they are energy-limited resources, actual reserve deployment from PSHs would cause the deviation of state-of-charge (SOC) from the scheduled value, which, once accumulated over time, could induce potential violations on SOC limits and cause non-dispatchability of PSHs. In recognizing this potential issue, it can become important to securing the reserve schedule of PSHs and other energy limited resources preventively in the day-ahead market clearing. To ensure reserve dispatchability of PSHs despite SOC deviations, this paper proposes the reserve secure constraints, which are cast as a distributionally robust chance-constrained formulation by judiciously introducing random parameters to describe deployment ratios of scheduled regulation reserve from PSHs. These constraints are converted into tractable second-order cone constraints, and further approximated as linear constraints to be compatible with the current ISO day-ahead market clearing model. A modified IEEE 118-bus system with multiple PSHs is adopted to verify the proposed approach.