One's courage or hope fails; one is very disappointed or dejected. For example, An hour before the picnic I heard thunder and my heart sank. This expression was first recorded in 1605 but was preceded in the 15th century by one's heart is at one's heels or in one's hose or in one's shoes. The present (and only surviving) usage was first recorded in 1605.
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.