“Lacking any… surface” (see Autolatry’s answer) in Jupiter is, first, dubious (a metallic hydrogen mantle is conjectured) and second, not very important per se. For example, Uranus and Neptune almost certainly have a relatively dense mantle with a sharp upper boundary, that doesn’t preclude these planets to have very long-living vortices in the atmosphere. How deep such a “surface” is situated may influence longevity of storms.
Important difference between Earth and giants planets is that Earth’s atmosphere is shallow and sparse, whereas giants’ atmospheres are thick and dense. Why does greater density prolong existence of vortices? Mainly because dense fluids tend to have lower kinematic viscosity (dynamic viscosity changes weakly on isothermal compression/decompression, whereas kinematic viscosity is dynamic viscosity divided by density). Dependence on depth is because a shallow fluid layer above a stationary solid exhibits greater shear rate (for similar motion speeds) and hence faster dissipation.