A high-precision measurement of the ¹³¹Cs→¹³¹Xe ground-to-ground-state electron-capture Q_EC-value was performed using the ISOLTRAP mass spectrometer at ISOLDE/CERN. The novel PI-ICR technique allowed to reach a relative mass precision δm/m of 1.4 ⋅ 10^{− 9}. A mass resolving power m/Δm exceeding 1 ⋅ 10⁷ was obtained in only 1s trapping time. Allowed electron-capture transitions with sub-keV or lower decay energies are of high interest for the direct determination of the ν_e mass. The new measurement improves the uncertainty on the ground-to-ground-state Q_EC-value by a factor 25 precluding the ¹³¹Cs→¹³¹Xe pair as a feasible candidate for the direct determination of the ν_e mass.