All 99+ Mustangs do that that I have seen. I have removed my defroster grill and observed that the hole that the clip goes into on that side is ever so slightly enlarged which causes the problem. You can gently pry out the defroster grill with a trim removal tool.
I am planning to use a small square of felt or thin rubber around the male part of the clip assembly to attempt to correct the situation. This should provide enough bulk and friction to keep the clip retained and the end of the defroster grill in place.