JBT may well be right- but if that doesn't work the octave mechanism may be sluggish;
Take the neck off the horn, hold down the G touch, and hold down the octave key. The body octave pip cup ought to flop back and forth without any friction when you touch it. On almost all horns the body octave pip cup is held closed by a lever on the upper end of the rod attached to the G touch when it is not depressed, as well as by the octave mechanism itself whenever the octave key is not depressed. When the octave key is depressed, the body pip cup is held closed by the G rod lever alone until the G touch is depressed- at that point the pip cup is no longer held down and force of the spring on the neck key closes the neck pip and simultaneously opens the body pip through the octave mechanism. When going the other way, releasing G (with the octave key depressed) closes the body pip via the lever on the rod and the neck pip is then forced open by the octave mechanism.
If the mechanism gets sluggish through the build up of crud and lack of lubrication (or damage) then there's a lag between when the G lever releases the body pip and the neck pip is closed and forces the body pip open via the spring on the neck octave key. When going from mid C to D players frequently press the octave key slightly ahead of the G touch and , with a sluggish mechanism, the result is a squirrely attack to the D as there's a fraction of a second when the neck pip is still open as it pushes the sluggish mechanism to open the body pip cup and close itself. Going down from E to D is fine since the octave pips are already in the correct positions (body open, neck closed).