It sounds like the derailleur is worn out.

Even with regular cleaning and oiling of the pivots, my Campagnolo Veloce rear derailleur had worn pivots after about 15,000 miles. The shifts were sloppy, with random gear noise when the chain wasn't centered on the cog. I sometimes had to shift two cogs and then back one to get the shift to work. I could wiggle the pulley assembly sideways with light finger pressure.

A new derailleur made a huge difference. The shifts were solid, and there's no play in the derailleur. (The new version has redesigned pivots, larger and moved farther apart. A much better design.)