Yep I also wondered why the peeling keeps going even if it's a scar tissue but maybe because of the special mobility and extension of the lips the superficial layer of the scar tissue, in lower quality than the rest, just never stops cracking.
You know it's like if our healty area of our lips was elastic, then our affected area was as solid as paper towel, isn't resistant enough to support the lips constraints.
On this pic we clearly see the difference of texture between these two areas on my bottom lip. It was like the affected area was just vermilion cells which are completely spread in the sense of the rubbing of lips together.