The gas dissipation from a protoplanetary disk is one of the key processes affecting planet formation, and it is widely accepted that it happens on timescales of a few million years for disks around single stars. In recent years, several protoplanetary disks have been discovered in multiple-star systems, and despite the complex environment in which they find themselves, some of them seem to be quite old, a situation that may favor planet formation. A clear example of this is the disk around HD 98800 B, a binary in a hierarchical quadruple stellar system, which at an ∼10 Myr age seems to still be holding significant amounts of gas. Here we present a 1D+1D model to compute the vertical structure and gas evolution of circumbinary disks in hierarchical triple-star systems considering different stellar and disk parameters. We show that tidal torques due to the inner binary, together with the truncation of the disk due to the external companion, strongly reduce the viscous accretion and expansion of the disk. Even allowing viscous accretion by tidal streams, disks in these kind of environments can survive for more than 10 Myr, depending on their properties, with photoevaporation being the main gas dissipation mechanism. We particularly apply our model to the circumbinary disk around HD 98800 B and confirm that its longevity, along with the current nonexistence of a disk around the companion binary HD 98800 A, can be explained with our model and by this mechanism.