It's a Miracle!
This is the law of the feast peace-offering that one will offer to Hashem: If he shall offer it for a thanksgiving-offering... (Lev. 7:11)
When someone has survived a life threatening situation he brings a Korban Todah, a thanksgiving offering, to express his gratitude and recognition that God saved him. This offering can be eaten for up to one day and one night.
A thanksgiving offering is a form of Korban Shelamim (peace offering), so why isn't it eaten for two days and a night like all other peace offerings?
We are surrounded by miracles all day long. In the Shemoneh Esrei we say, "Thank you God for Your miracles that are with us every day." One who brings a thanksgiving offering has become aware of one solitary miracle while remaining oblivious to all the others. Therefore, a thanksgiving offering may be eaten for only one day since tomorrow there will be other miracles for which to be grateful!
God is constantly performing miracles, whether they are obvious or hidden. We are surrounded by them. When flying in an airplane or just crossing the street, God holds our hand and saves us from possible danger. A Czarist official in Russia once asked the Netziv, Rabbi of Volozhin, why many verses in Tehillim (Psalms) call upon the nations to praise God for his salvation of Israel. Should it not be the Jews who praise God for saving them?! The Netziv replied, "We have no way of knowing the extent of your conspiracies against us. Only you know how many times you have plotted against us, but have been thwarted by God. Since you are far more conscious than we are of the magnitude of God's miraculous salvations, only you can appreciate the full extent of His greatness."
1. Imrei Emes (Quoted in Artscroll stone Chumash). The Ha'amek Davar gives another answer: There is much to be eaten in such a short time span. Therefore, by limiting the eating period to just one day, you'll have to invite many people to help you finish it and the miracle will become known to all!