The adaptive cross approximation (ACA) is considered for matrix structures where error control is lost. A weighted average form of the adaptive cross approximation is presented that mitigates the loss of error control. In the averaged ACA algorithm, the ACA is applied to a matrix comprising linear combinations of the rows and columns of the original matrix. An efficient implementation of the weighted average algorithm is outlined. The performance of the ACA and averaged ACA are examined for both static and time-harmonic integral equation solutions of problems for which loss of error control by the ACA is observed. The behaviors of the ACA and averaged ACA are compared and discussed, and the averaged ACA is observed to maintain error control for many matrices for which the ACA fails.