I am using pop up heads - Rainbird Maxi-Paws. This is what the guy put in when it was installed several years ago. Of course, I have replaced many of the heads that have stopped working from time to time.
Are the newer rotor types better?
Maxi paws are fine, just got to clean them out from time to time when they stop rotating
There are other possibilities of what's wrong. But the highest probability is a broken pipe / broken sprinkler fitting.
Unfortunately you can't turn those impact heads off. Time to get your shorts on and walk out there looking for wet mushy spots when the zone is running.