Does the Sampling Rate affect the syncing process to a video source?
You can tell which one gets out of synch like this:

Set up your camera and your phone like you usually do. Put a clock that shows seconds right in front of the camera. Then, even though this sounds boring, record yourself counting off the seconds.

Synchronize the video and audio in Premiere Pro like you usually do. When they get out of synch, check whether the video lost a second, or whether the audio lost a second. You should be able to tell based on the repetitive rhythm.

Then, as @AJHenderson pointed out, you should replace the piece of equipment that failed. I agree that a camera that can accept external audio input is probably the best option, though it's expensive.