But Hibernian have successfully challenged the red card handed to midfielder Marvin Bartley following his challenge on Ayr’s Jamie Adams.
Saints boss Tommy Wright decided to challenge the bookings given to his men during their 1-0 win over Hearts on Saturday.
Referee John Beaton cautioned Cummins - who scored the Perth side’s second-half winner - for simulation following a challenge by Igor Rossi 14 minutes in before giving the same treatment to substitute Kane late in the game after he also hit the deck while tussling with Perry Kitchen.
Wright has warned his men they will be fined if they go to ground too easily, but defended the pair on this occasion, insisting they had been “wrongly cautioned”.
However, the Scottish Football Association’s judicial panel rejected both appeals after upholding Beaton’s original decisions.
But Easter Road chiefs have had more luck after successfully contesting Bartley’s dismissal.
He slid in hard on Ayr midfielder during the Leith side’s 2-1 home defeat, but the panel agreed match official Nick Walsh had over-reacted.
The red card shown to the former Leyton Orient battler has been reduced to a yellow, freeing him to face Queen of the South in this Saturday’s showdown between the Ladbrokes Championship’s top two sides at Palmerston.