One possibility is that the shift lever is not tight. When you shift to a larger cog, if you hold the lever in place, will the chain stay in place? And then when you let go of the lever, the chain moves back down to the small cogs and the lever moves by itself? If so, tighten the screw/bolt that holds the lever on. If it is too tight, you will not be able to move the lever with your hand. But just a little bit looser than that, it will hold the lever in place after you shift.