Longevity of entrapped air is an outstanding problem for using superhydrophobic coatings in submersible applications. Under pressure and flowing water, the air micropockets eventually dissolve into the ambient water or burst and diminish. Herein, we analyze from first principles a simple mass transfer problem. We introduce an effective slip to a Blasius boundary layer, and solve the hydrodynamic equations. A slowly evolving, non-similar solution is found. We then introduce the hydrodynamic solution to the two-dimensional problem of alternating solid-water and air-water interfaces to determine the convective mass transfer of air's dissolution into water. This situation simulates spanwise microridges, which is one of the geometries used for producing superhydrophobic surfaces. The mass-transfer problem has no similarity solution but is solvable using approximate integral methods. A mass-transfer solution is achieved as a function of the surface geometry (or gas area fraction), Reynolds number, and Schmidt number. The analytical results are compared to numerical simulations of the laminar Navier-Stokes equations. Longevity, or time-dependent hydrophobicity, can be estimated from the resulting mass-transfer correlation.