Formation of a hydrated superficial layer early in the history of the Earth and Earth-like planets may occur by extensive serpentinization of mantle rocks by water, similar to that still active at present-day in slow-spreading oceanic plates. We investigated the lifetime of this buoyant and weak hydrated "crust" with 2D numerical simulations of mantle convection. Three regimes of preservation of the hydrated crust exist as a function of its thickness and buoyancy, both of which depend on the intensity of hydration. Firstly, an unlikely regime for the Earth is that where a thick buoyant crust (>100 km) can form a convective lid above the mantle. Secondly, a regime exists where weakly hydrated crust disappears through convection at a rate similar to the reference null hydration model. The lag time before which convection starts decreases with increasing thickness, decreasing the potential survival of the hydrated crust. Finally, a regime is found where rafts of highly hydrated crust of intermediate thickness are preserved at the surface. This regime is possible on the early Earth, and the survival time of the hydrated crust is proportional to its thickness. The present models indicate that a 50 km-thick fully serpentinized layer may have formed and survived over about 1 Gyr at the surface the early Earth, and could have favored the formation of the first differentiated felsic crust by partial melting.