It could mean a sign that is delicate or easily broken, similar to the elements in the Christmas story which might be seen as precious and in need of gentle handling, like the baby Jesus in the manger.
Well, perhaps it refers to a sign that has a tenuous or weak quality, just as some aspects of the Christmas story can seem somewhat ethereal or hard to fully grasp. For example, the idea of angels appearing to shepherds. It's a fragile concept in a way, and the sign might be related to that sense of something that is both important but not entirely of this world.
The 'fragile sign like the christmas story' might imply a symbol or indication that is as vulnerable as the themes in the Christmas story. The Christmas story is full of hope and new beginnings, but also has elements of danger and uncertainty, like Mary and Joseph's journey. So the sign could be something that represents a state of being that is both full of potential but also at risk, much like the characters and events in the Christmas tale.