According to 1453 by Crowley Mehmed stopped the looting because he envisaged Constantinople as the new capitol of his empire. He had to quickly put his soldiers under control to keep them from pillaging and destroying what he wanted to be the glistening jewel of the Ottomans. Mehmed was also very interested in classical Greeks and Romans and liked to imagine himself as a new Alexander the Great, or creating a new Roman Empire. Ergo he put a lot of value into the history of the city and didn't want to see it destroyed.

Clarification: Are you asking why he permitted any looting, why didn't he permit more looting, or why exactly 3 days of looting?

The city was at a strategic cross point between Europe and Asia so when the turks invaded they meant to annex the city into the Ottoman empire. The Sultan realize that the city would not be of use if its destroyed so he ordered his army to stop looting. Im heavily paraphrasing a documentary I saw months ago but i believe I'm right.