I just spent three days troubleshooting this problem, so I thought I’d share the solution in case anybody else is struggling with it.
The latest iPhones shoot video with variable frame rates, but Premiere Pro cannot handle variable frame rates, so when you import iPhone video into Premiere, the video appears to skip, stutter or hang up on a particular frame.
Apparently there is no fix for this problem within Premiere Pro, and you cannot tweak your iPhone’s settings to shoot solely in constant frame rates. Instead, you have to convert the video to constant frame rates using third-party software, HandBrake, which is available for free at http://handbrake.fr.
I explained the whole process in this Google document: