I haven’t tried monkeybort’s resize-in-steps suggestion; perhaps I should.
One thing that I do to try to keep sharpness after a resize is to apply a sharpening technique. Photoshop has all sorts of sharpeners – if I’m in a hurry, I’ll use the built-in Sharpen Edges or the Smart Sharpen filters. If I really want to control the sharpening, I’ll use a different process. I usually sharpen right before final output.