The subject says it: Are the Palm Trees and Palaces of the supply strictly limited?
We had a situation, where a player obtained the Djinn Enki an built a Palm Tree nearly every turn (paying a Slave or Elder is not so costly), so the Supply was exhausted earlier, than the end of the game came.
They are both limited. The rules specifically say you don't put one on if you run out. See the Tile Actions section of the rules.