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The valley degree of freedom is a sought-after quantum number in monolayer transition-metal dichalcogenides. Similar to the spins of electrons and holes, the valley degree of freedom is not a conserved quantity and excitons lose their original helicity over time. Valley depolarization of excitons in monolayer transition-metal dichalcogenides due to long-range electron-hole exchange typically takes a few ps at low temperatures. Exceptions to this behavior are monolayers MoSe2 and MoTe₂ wherein the depolarization is much faster. We elucidate the enigmatic anomaly of these materials, finding that it originates from Rashba-induced coupling of the dark and bright exciton branches next to their degeneracy point. When photoexcited excitons scatter during their energy relaxation between states next to the degeneracy region, they reach the light cone after losing the initial helicity. The valley depolarization is not as fast in monolayers WSe₂, WS₂ and likely MoS₂ wherein the Rashba-induced coupling is negligible.