President Jacob Zuma had given Phiyega until yesterday to motivate why she should remain in her position.
This after the Marikana Commission of Inquiry - which investigated the deaths of 34 miners at the Lonmin mine in 2012 - recommended an inquiry be held into her ability to hold office.
The Institute's Gareth Newham believes Phiyega disregarded her legal obligation to minimise the loss of lives and avoid injury at Marikana.
"We already know that Phiyega is not honest and cannot be trusted to exercise her authority in the best interest of the people of South Africa", he said.
"So she is most likely to use her powers to undermine or hinder such investigations into and actions against police officers under her command", Newham said.
Meanwhile the Presidency says Phiyega has failed to meet the 10 O'Clock deadline last night to submit her letter to the president.
Her office has yet to give reasons as to why she missed the deadline. It is not clear also the reasons for her being mum.
The report on Marikana events found that the police's tactical response option to the the thousands of striking armed Lonmin mineworkers failed.
It also found that police lacked command.
(Photo: Gallo images)
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