Former Cosatu general secretary Zwelinzima Vavi and EFF leader Julius Malema are plotting to overthr.
The national play-offs were scheduled to take place at three venues in Ekurhuleni - Mehlareng Stadium, Sinaba Stadium in Daveyton and Makhulong Stadium - from June 24 to 30.
Safa competitions director Balebetse Monnakgotla said a new date has to be set for the play-offs when the top two clubs will be promoted to the National First Division next season.
So far only three provinces have determined their winners without boardroom disputes - Gauteng (FC Vardos), Eastern Cape (Mthatha Bucks) and Mpumalanga (Mbombela United).
Limpopo, Free State, Northern Cape, KwaZulu-Natal, Western Cape and North West have outstanding cases that are being dealt with by the disciplinary committee.
"Our disciplinary committee members are busy with protests that were lodged by clubs in various provinces, hence the decision was taken to postpone the national play-offs indefinitely," said Monnakgotla. "We will make an announcement only once all the cases are resolved, hopefully by next Tuesday."
Meanwhile, Mthatha Bucks are confident of gaining promotion to the NFD, with Velile Jaloyi in charge of the technical staff.
Jaloyi is the former coach of Blackburn Rovers, the only Eastern Cape side campaigning in the NFD.