Mosiah 21

Paul wrote the Corinthians -

...I rejoice, not that ye were made sorry, but that ye sorrowed to repentance: for ye were made sorry after a godly manner, that ye might receive damage by us in nothing.
10 For godly sorrow worketh repentance to salvation not to be repented of: but the sorrow of the world worketh death." (New Testament | 2 Corinthians 7:9 - 10)

The Lord is interested in the type of sorrow Godly sorrow) that brings repentance sufficient to bring the gift of salvation. We see this process somewhat amongst the people of Limhi as -

"...there was a great mourning and lamentation among the people of Limhi..." (Book of Mormon | Mosiah 21:9)

And -

"...there were a great many widows in the land, and they did cry mightily from day to day..." (Book of Mormon | Mosiah 21:10)

This sorrow did not seem sufficient. After a time -

"...they did humble themselves even to the dust, subjecting themselves to the yoke of bondage, submitting themselves to be smitten, and to be driven to and fro, and burdened, according to the desires of their enemies.
14 And they did humble themselves even in the depths of humility; and they did cry mightily to God; yea, even all the day long did they cry unto their God that he would deliver them out of their afflictions." (Book of Mormon | Mosiah 21:13 - 14)

It seems at this point the people are beginning to experience Godly sorrow, but -

"...the Lord was slow to hear their cry because of their iniquities; nevertheless the Lord did hear their cries, and began to soften the hearts of the Lamanites that they began to ease their burdens; yet the Lord did not see fit to deliver them out of bondage.
16 And it came to pass that they began to prosper by degrees in the land..." (Book of Mormon | Mosiah 21:15 - 16)

Godly sorrow unto repentance then must be sufficient to never fall away again or in other words sufficient unto salvation. Though the people continued to experience Godly sorrow, patience and show true repentance, the Lord was working in the hearts of those in Zarahemla to send a rescue party. Later, when their repentance was sufficient unto salvation we learn of their deliverance.