Higher-derivative corrections to cosmological effective actions in string theory are largely constrained by T-duality, but have been computed hitherto only to the first few orders in the string scale α′. The functional renormalization group, in conjunction with the strong constraints imposed by T-duality, allows us to derive cosmological effective actions to all orders in α′ while avoiding "truncations"of the theory space. We show that the resulting higher-derivative α′-corrections forbid the existence of de Sitter vacua, at least in regimes where string-loop corrections can be neglected. Our findings thus support the no-de Sitter swampland conjecture in the presence of all-order effects in α′.