Rear derailleur has trouble switching gears on the way up, but works perfectly on the way down?
This sounds like classic derailleur cable friction. The cable gets stuck inside the housing and stops or delays the derailleur moving to smaller sprockets. This is caused by dirt contaminating the housing, or perhaps corrosion of the cable.

The fix is to remove, clean, re-lube and re-install the cable, or replace the cable and housing altogether.