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Using self-consistent mean-field and functional renormalization-group approaches, we show that s-wave pairing symmetry is robust in the heavily electron-doped iron chalcogenides AFe_{2-x}Se_{2}, where A=K,​Cs. Recent neutron scattering experiments suggest that the effective nearest-neighbor spin exchange may be ferromagnetic in chalcogenides. This is different from the iron pnictides, where the nearest-neighbor magnetic exchange coupling is believed to be antiferromagnetic and leads to strong competition between s-wave and d-wave pairing in the electron-overdoped region. Our finding of a robust s-wave pairing in (K,​Cs)Fe_{2-x}Se_{2} differs from the d-wave pairing result obtained by other theories where nonlocal bare interaction terms and the next-to-nearest-neighbor J_{2} term are underestimated. Detecting the pairing symmetry in (K,​Cs)Fe_{2-x}Se_{2} may hence provide important insights regarding the mechanism of superconducting pairing in iron-based superconductors.