For a reaction A + B --> C + D, let the limiting reactant be A and the excess reactant be B. The amount of B that reacts is dependent solely on the amount of A that is available to take part in the reaction. This is what makes A the limiting reagent, the progress of the reaction is limited on the amount of A available.
If the limiting reagent is impure, the reaction yield can only be equal to the purity of the limiting reagent. Assume that the limiting reagent A has a purity of X%. The reaction yield in this case cannot exceed X%. Even if there is an amount of reagent B left to take part in the reaction, the other reagent is not available for the reaction to proceed.