The statue of Hermione at Paulina's house is not a real statue that comes to life by a miracle, it is actually Hermione herself. King Leontes thought she was dead (he had seen her 'corpse' - in reality just her unconscious body) but in fact she had been concealed by Paulina for the last sixteen years.
There are lots of hints the in preceeding scenes that Hermione is in fact alive. Pauline makes sure the King promises to marry no-one except a woman she shall choose, who shall be as good as the late Queen - although, of course, no such woman exists. She is preparing him to receive his wife back. She has been regularly visiting the building where the 'statue' was while it was under construction - in fact, to see Hermione and presumably bring her food. The statue is described as looking older than Hermione was when she died - by about sixteen years. And in the final scene, when the statue is presented to the company, Paulina warns the King not to let his imagination run away with him so that he thinks the statue is breathing or moving. All this is to trick King Leontes for a few more moments before he realises the wonderful truth: His innocent wife, whom he thought he had killed (by grief at his actions) is in fact alive.
The miracle in this play is not a living statue, but the fate that has brought a scattered family and broken friendship back together after sixteen years.