Torah is "Our life, and the length of our days." It is not possible for something to be called 'living' if it's alive only at certain times of the day, week or year. Life is constant at all times, and without pause.
Not a single part of a Jew's day -- whether in the realm of thought, speech, or action -- is disconnected from Torah. In the words of the Sages: "All your deeds should be for the sake of Heaven." All a person's activities, without exception, must be infused with the vibrance of his or her relationship with G-d.
The Talmud compares a Jew without Torah to a fish out of water. A fish, however, can survive temporarily on dry land, whereas a Jew cannot thrive even one moment outside the realm of G-dliness. In the words of King David: "I have placed the Lord before me at all times" -- literally, every single moment of one's life.