What characteristics of stars determine the length of a star's life?
Mass of the star that determines its life.With uge mass there will be very high premature in the core and the rate of fusion will be very high .They not only fuse hydrogen to helium but to other heavy elements"Those fusion reactions create the elements silicon, sulfur, chlorine, argon, sodium, potassium, calcium, scandium, titanium and iron peak elements: vanadium, chromium, manganese, iron, cobalt, and nickel. These are called "primary elements", in that they can be fused from pure hydrogen and helium in massive stars." wikipedia
The length of a star's life is determined by its core temperature which is determined by its mass.
Smaller stars, like our Sun, have relatively cool core temperatures. They fuse Hydrogen into Helium mainly by the proton-proton chain reaction which is relatively slow. This means that they have a long life. A star the size of our Sun has a lifetime of around 10 billion years.
Stars which are more massive than 8 solar masses have much hotter cores. They use the Carbon-Nitrogen-Oxygen (CNO) cycle to fuse Hydrogen into Helium. The CNO cycle is very fast and gets faster as the core gets hotter. Massive stars only have much shorter lifetimes measured in millions of years.
So, the larger the star the shorter its lifetime.