Originally banned for eight years, reduced to six on appeal, Platini took further court action in May and had the ban cut to four.
But Platini's lawyers say they still have not been told why the decision was made.
In a letter addressed to CAS, the former French footballer's lawyers demanded an explanation "in as brief a time as possible" and branded CAS's behaviour "unacceptable".
Platini was sentenced over a 1.8 million euros (2 million Swiss francs, $2 million) payment made to him by Sepp Blatter in 2011.