A time reversing or phase conjugate array operating in a random medium has been shown to focus acoustic radiation better than an equivalent array operating in a nonrefractive medium, making such arrays attractive for a large class of underwater acoustic problems. The present work extends this result to include the lifetime of the array's focus, and shallow-water random refraction. Analytic predictions of focal properties, based on the parabolic approximation to the second moment of the Green's function connecting the source with the array, are made for acoustic propagation through an unbounded dynamic random medium. The necessary projected autocorrelation function for the spatial and temporal evolution of the acoustic medium has been constructed from available oceanographic shallow-water fluctuation statistics. Focus size and focus lifetime are predicted to depend on acoustic frequency, source--array range, and array size. Focus lifetime predictions suggest that there is substantial opportunity for retrofocusing application of this technology. Influence of the ocean surface and deterministic water column variations will be addressed in future research.