A plea to God for life usually stems from a basic human desire to survive, but it can also reveal a much deeper spiritual motivation. Asking for His compassion to sustain one's life is intimately tied to a profound love for the Torah. The desire to live is not merely about physical existence, but is deeply rooted in the joy of studying and engaging with His teachings.
The primary approach among commentators is that deep devotion to the Torah makes a person worthy of receiving special compassion and kindness from God. This is particularly true when an individual finds their absolute delight in the Torah, having no other source of comfort or pleasure [אבן עזרא, מצודת דוד, ביאור שטיינזלץ]. However, others explain that the Torah is not merely a merit that earns a person the right to live, but rather the very purpose of life itself. From this perspective, the entire request for survival is driven by the desire to continue observing the Torah, and the person wishes to live solely for its sake [רד"ק, מאירי].
There is an additional, practical reason why a person dedicated to the Torah requires a special measure of divine mercy. Intense study and engagement physically exhausts a person, draining their natural strength. Because of this physical toll, the learner depends on an extra infusion of God's compassion just to sustain their physical survival, even though the teachings themselves are fundamentally a source of life [מלבי"ם].