At idle, the kickdown cable should still be pulling on the linkage. It should not be loose.
A good cable adjusted with a 1-2mm gap at idle will maintain spring tension on the plastic link, which takes up any slop in the ball joints. If your plastic link is loose at idle, then your kickdown cable is not pulling on the linkage.
Too loose at idle means the gearbox thinks you're accelerating more gently than you actually are, and it'll upshift/lockup early rather than holding the lower gear.
I can think of 2 reasons why the kickdown cable might not be pulling on the linkage at idle:
-Binding pivot point on the cable to link lever (unlikely but worth checking)
-Stretched kickdown cable (most likely). If you disconnect the cable (remove the pivot pin from the fork), the cable should pull itself into the sheath until the little stopper hits the outer cable. If your cable has stretched, it will run out of spring before the stopper hits the outer cable, leaving the cable loose with a gap between the stopper and the outer cable.
If it runs out of spring and leaves a gap, then you'll need to take that gap into account when setting the stopper position at idle. Add 1-2mm to the gap, and use that as your stopper-to-outer cable distance.
If it's stretched, it might be that the other end of the cable is failing.
Here's a thread where @petervanschie had a cable repaired at a motorcycle shop. Just be aware that
@Tbizzy23 has a petrol engine, so their kickdown cable is different (doesn't have a forked end).