I have a Kimber stainless target in 10mm. I purchased this pistol used, but in excellent shape.
It does have one problem though. Sometimes randomly when shooting, the trigger hangs up and the gun doesnt fire until you release the pressure against the trigger and squeeze it again.
Doesnt happen all the time. Maybe 5 times in the last 300 rounds.
sounds like your disconnector isn't moving freely....either that, or your sear spring needs to be replaced.
try giving the frame guts a thorough cleaning, re-lube and test fire. If it's still doing it, replace the spring.
I had this happen on my Les Baer and again on my SA. (LB was a worn out sear spring, the SA was a rough disconnector that needed to be polished some)
eta: just thought of something--dry fire it, and hold the trigger back. Cycle the slide, then release the trigger. Did you hear a click? You should hear it when the trigger moves forward a tiny bit. If you don't hear it and your pistol has an adjustable trigger, backing the set screw out a quarter turn should fix it.