What is the name of the membrane that holds the coils of the small intestine together

Its name is Mesentery.

Explanation:

This membrane holds the coils of small intestines towards the abdominal wall. It is made up layers (two) of Peritonium which contains jejunum and ileum, nerves, lymph nodes and fats. This membrane can also be infected which is known as Mesentric Lymphadenitis which is a common viral infection, causing the mesentery to move at the back of the intestinal wall causing inflammation.