On its first day, around 500 people a second were estimated to be trying to access the site.
It contains the records of 400 million people dating back 500 years.
They have been gathered by the Church for more than a century for members, who are required to trace their family roots as part of their faith.
Quadruple overload
The site was down for six hours after the crash on Monday, forcing its high-tech partner, IBM, to add a support computer to handle the traffic.
IBM spokeswoman Jan Walbridge said: "It's triple, quadruple what they anticipated.
"They did plan for a back-up system, but they didn't think they'd have to use it so soon."
Family trees
Genealogy is one of the most popular subjects on the Internet with more than 40,000 different sites dedicated to family searches.
For Mormons, tracing family trees also forms an important part of their religious duties.
The Mormons, or the Church of Jesus Christ of Latter-Day Saints, first began compiling parish records from across the world since 1894.
Microfilm copies of the records, which are stored in a vault in the Wasatch Mountains near Salt Lake City, were used to compile the massive Mormon database.
The Mormons say they plan to add a further 200 million names to its FamilySearch database by the end of the year.
Burke's breaks taboo
(23 May 99 | UK)
FamilySearch
Ancestry.com
The Church of the Latter Day Saints
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