The decision means Bosnia may not be able to carry on playing their Euro 2012 qualifiers after UEFA warned their presidential system had to change for their national team and clubs to avoid a suspension coming into effect on Friday.
They are fourth in Group D with seven points from four matches after Saturday's 2-1 home win over Romania.
The outcome of the NFSBiH Congress, with 28 of the body's 53 delegates voting against the motion, means that it failed to replace a rotating three-man presidential system which operates on an ethnic basis.
Under the current statutes, a Serb, a Croat and an ethnic Muslim take turns in holding the post.
"I feel no personal responsibility for the failure of the Congress to pass the new statutes since I did not make this decision alone," NFSBiH Serb presidency member Bogdan Ceko, who voted against the reform, told reporters.
Explaining their reluctance to comply with UEFA and FIFA, NFSBiH officials said they were concerned that an ethnic group could be outvoted if the complex system was replaced by a one-man presidency.
In Bosnia, football is one of many spheres where political and ethnic divisions have overshadowed efforts to bring together a country torn apart by a 1992-95 war.
The NFSBiH was formed in 2002 as an institution coordinating the football associations from Bosnia's two autonomous regions, the Serb Republic and the cantonal Muslim-Croat federation.
The body's members are chosen partly on ethnic criteria and the principle has long since triggered protests from fans across the country, while some players have boycotted the national team.
"What we saw today was a clear sign that politics is deeply rooted in sports," ethnic Muslim delegate Hasim Zuko said.
"Suspension may be the best solution to help us start building this sport from scratch with new people in the presidency."
A group of fans protested in front of the central Sarajevo hotel where the Congress was held and one of their leaders agreed that a suspension may be worthwhile if it helps Bosnia's soccer get back on track.
"If the burial of Bosnian soccer is the price we have to pay for the departure of NFSBiH then we are ready to pay it," said Nizar Altimori of the BH Fanaticos group.
Sports commentator Sinan Sinanovic said he hoped the international governing bodies could set up an interim soccer body in Bosnia to adopt new statutes by June 3, when the Bosnians are due to visit Romania in their next Euro qualifier.
"I hope that FIFA and UEFA will help us find some new faces who are not politically compromised to lead the football federation and I still want to believe that the national team and football clubs will not be punished," he said.
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