Los Blancos now sit 16 points behind leaders FC Barcelona, after they drew 2-2 with Celta Vigo last weekend.
And after a disappointing 2-2 draw at home against Numancia on Wednesday, the questions over Zidane's future have grown. It has gone four matches without a win.
Madrid, which has a game in hand, is only fourth in the standings, behind Valencia and Atletico Madrid.
Zidane's Madrid welcome sixth-placed Villarreal to the Santiago Bernabeu on Saturday, and despite having little chance of winning LaLiga are still in the running in the Copa del Rey and face PSG in the ChampionsLeague round of 16.
Referee Alberto Undiano Mallenco was unmoved on both occasions, while Madrid was further frustrated by a poor one-on-one miss by Ronaldo and some good work by Villarreal goalkeeper Sergio Asenjo.
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Republican leaders were largely silent, though House Speaker Paul Ryan said the vulgar language was "very unfortunate, unhelpful". The sources spoke on condition of anonymity because they weren't authorized to publicly describe the conversation.
Ronaldo also had a chance just moments before halftime.
He made an even better stop to palm Ronaldo's 25-yard dipping free-kick over the top via the crossbar, before the Portugal captain wastefully dinked over Asenjo and wide of the left post after latching onto Luka Modric's throughball.
Las Palmas could have left the bottom of the standings with a draw but it never challenged the Catalan host at Montilivi Stadium, seeing its winless streak reach seven matches in all competitions.
Christian Stuani opened the scoring for Girona from a penalty kick midway through the first half, and the other five came in a 22-minute span in the second period.