$Mn^{2+}$ has an electronic configuration of $1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{5}4s^{0}$. To goto $Mn^{3+}$ state the electron has to be taken out from stable d5orbital whichis half filled and requires very high ionisation energy. In case of $Fe^{2+}$ ion,the third electron is taken out from $3d^{6}$configuration which results inmore stable $3d^{5}$configuration.