Under Bracewell, New Zealand have won just three of 12 Tests, and public calls for his dismissal have been growing since the side was trounced in the recent two-Test series against Australia.
But New Zealand Cricket chief executive told the New Zealand Herald that Bracewell had had his initial two-year contract extended to July 2007.
"We decided we wanted to back him more and give him the job security he needed to be successful in the position," Snedden said on Thursday.
He said it was important Bracewell had enough job security to prepare for long-term and short-term objectives, something that wasn't possible with a 24-month contract.
"The problem with a two-year cycle is that we often changed for change's sake and ended up getting someone who would just repeat the same old mistakes."
Despite New Zealand's dismal Test performances under Bracewell, as a one-day unit the record is an impressive 18 wins from 21 completed matches.