A microfluidic oscillatory cross-slot flow is used to visualize birefringent strands in dilute polystyrene solutions with high temporal resolution, focusing specifically on reversals in the flow direction. Due to polymer conformation hysteresis, the elastic strands are slow to relax and demonstrate a compressive modulus, resulting in a "buckling instability." An elastic loop of birefringence forms in an exit channel of the cross, seeding the development of a new birefringent strand in the perpendicular direction. These observations have major relevance to cyclic flows of polymer solutions (e.g., porous media flows where stagnation points are present) and for finitely extensible nonlinear elastic dumbbell modeling of such flows.