Esther tells Achashveirosh in the name of Mordechai of a plot to assassinate him (Achashveirosh). They investigate, and stop the would-be assassins. And then... nothing? Why didn't Achashveirosh reward Mordechai right then?
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The Malbim on Megillas Esther (2:23, page 61 in the aforelinked book) asks this question, and concludes that this is one of the numerous miracles surrounding the story of Esther's ascent to power. It would have been much more normal for the debt to have been paid off immediately, and his not doing so is simply an act of G-d.
Since Mordechai did not tell the King himself, Achashveirosh felt beholden to Esther for saving his life, and in addition Hashem put into the mind of Achashveirosh not to pay Mordechai right away in order to save it for later when it was needed.