Whereas magnetic frustration is typically associated with local-moment magnets in special geometric arrangements, here we show that SrCo2As2 is a candidate for frustrated itinerant magnetism. Using inelastic neutron scattering (INS), we find that antiferromagnetic (AF) spin fluctuations develop in the square Co layers of SrCo2As2 below T approximate to 100 K centered at the stripe-type AF propagation vector of (1/2, 1/2), and that their development is concomitant with a suppression of the uniform magnetic susceptibility determined via magnetization measurements. We interpret this switch in spectral weight as signaling a temperature-induced crossover from an instability toward ferromagnetism ordering to an instability toward stripe-type AF ordering on cooling, and show results from Monte-Carlo simulations for a J(1)-J(2) Heisenberg model that illustrates how the crossover develops as a function of the frustration ratio -J(1)/(2J(2)). By putting our INS data on an absolute scale, we quantitatively compare them and our magnetization data to exact-diagonalization calculations for the J(1)-J(2) model (N. Shannon et al., Eur. Phys. J. B 38, 599, 2004) and show that the calculations predict a lower level of magnetic frustration than indicated by experiment. We trace this discrepancy to the large energy scale of the fluctuations (J(avg) greater than or similar to 75 meV), which, in addition to the steep dispersion, is more characteristic of itinerant magnetism.