Originally Posted by cny-bikeman

First you need to determine that the chain is actually dropping from the 2nd smallest cog to the smallest, rather than "skipping" when you apply high pedal pressure when on the smallest, which means that cog is worn. If it is dropping it is NOT the B tension screw, which affects only shifting onto a cog, not staying on it, and neither is it the limit screw. The most likely cause is cable/housing friction, as the derailleur cannot shift to the small cog unless the shifter is in that position. What you are likely experiencing is a delayed shift to the small cog. Putting pressure on the pedals would flex the frame enough to induce the cable to move the rest of the way.