You will need to buy a test light and ride ski until it won't start, then using the test light, begin at the battery and work "up the line" to see where the 12 volts is dropping out.
I know you said you have a new battery and terminals (and I suspect the new terminals). If they were not soldered in and well insulated, that could be the problem. That electrical system is in a very harsh environment. That is why most of it is inside a sealed box. Inside that box is also a fuse that can be your trouble. If the fuse is loose, or has a bit of corrosion on the lugs, it could short when hot, then make contact when cooled.
You have a simple problem I'm certain, just gonna take some detective work to find it. Go here;http://216.37.204.206/Mcmart/Kawasaki_OEM/KawasakiPWC.asp?Type=12&A=45 look under "ignition system" and "electrical equipment" for some help as to where to look. It is not a wiring diagram, but will help.
Also, unplug all the connectors to the ignition, look for burned terminals, ones that may have been hot, or any green corrosion. Clean or repair those if any, then spray the terminals with WD40 and re-connect.
If you have to go inside the electrical case, be sure it is dry and well sealed when you re-install it. It is possible your power drop is in there at the starter solenoid.
First check for power at the battery, past the terminals, the at the starter connection (on the starter itself, its a bit hard to get to, but that connection can loosen). Then work up to the solenoid, and ignition and kill switches.