It is difficult to know from your question if you would like to know what keeps the cell alive in terms of nutrients and substances or what in the animal system is in charge of deciding when a cell should live or die. I will try to answer both.

The cell is the structural and functional unit of all living organisms. Some organisms, such as bacteria are unicellular, consisting of a single cell. Other organisms, such as humans are multicellular. The cell is the smallest living unit capable of growth, movement and reproduction. Whatever their function, cells are constantly being recreated from other cells by a complex process of division known as mitosis. In most animals and in humans, cells that are specialized in a specific function, group together to form tissues, and tissues become further aggregated to form organs. During animal development, organs grow to a fixed size and shape.

Organ development typically begins with a rapid growth phase followed by a gradual decline in growth rate as the organ matures. This development is controlled by a complex system of cell-signaling and by different materials and organelles inside the already existing cells.

To survive, every cell must have a constant supply of vital substances such as sugar, minerals, and oxygen, and dispose of waste products, all carried back and forth by the blood cells. Without these substances, cells would die in a very short period of time. If too many cells in an organ die too quickly, the organ itself may be damaged.

But all cells will eventually die. A special process called Programmed cell death is a normal physiological form of cell death that plays a key role both in the maintenance of adult tissues and in embryonic development. In adults, programmed cell death is responsible for balancing cell proliferation and maintaining constant cell numbers in the tissues. Also, Programmed cell death is one of the first lines of defense against cancer and infection by invaders such as viruses.

Cell survival times in the human or animal body vary from a few minutes for certain intestinal cells to about 4 months for red blood cells and many years for some nerve cells.

How do developing animal cells decide whether to live or die, grow or stop growing, proliferate or stop proliferating into, or differentiate into one cell type rather than another? Scientists have discovered that these decisions are determined by a combination of cell-cell interactions. They have identified a number of the molecules that control these decisions in different organs. And there is a lot of research done in this field today.