[RCW]

Log in to Kawasaki.com and go to the parts diagrams for your machine. There are two diagrams that you want to look at, the first is the gear change mechanism, and the second is the change drum/shift fork.

What you want to pay attention to is how the shift lever actuates a cam that rolls the shift drum. I suspect your problem is the spring that holds the change position lever to the gear change drum cam, or the bolt that holds the cam to the drum is loose. Either of the three rollers that index the change cam can be the problem too, but not likely if you can shift and hold all the other gears.

Take your service/repair manual and go to the section on the transmission and shift mechanism and you will find that it is not a difficult fix. Do not attempt it without the manual.