In this work we study experimentally the lifetime of oil droplets pressed by buoyancy against a large oil/water interface, in a system containing protein (bovine serum albumin). The stability of the drops depends strongly on their size, which can be explained with the hydrodynamics of thinning of the gap region. Two distinct size intervals with different thinning regimes may be discerned: (i) Very small drops (below similar to 20 mu m). They remain practically nondeformed up to coalescence; in this case the lifetime diminishes with increase of the drop radius. The latter trend may be described qualitatively in terms of the Taylor law (or mixed Stokes-Taylor law) for viscous resistance. (ii) Large drops. They form films, and the lifetime rises with the increase of the size, which complies with the Reynolds law for the friction in the gap. The overall dependence of the lifetime on the drop radius passes through a shallow and broad minimum-here for the first time this is proved by direct measurement in a real system: only the drop size is varied with all other experimental conditions being the same.