Problem appears to be fixed. Kawasaki rep said it sounded like engine was only running on one cylinder (it's a twin). So, he suggested to pull the plug wire on each side (one at a time) and see if the engine rpm's dropped (as though on one cylinder) or quit entirely. They should drop but keep running since the other cylinder is still plugged in.
Engine quit with the right wire pulled, so we ordered an ignition coil for the left side and since it's been installed no more problems.