This is a great question! When we talk about the sun as being renewable, we are reflecting a human-scale understanding of time. The sun is about four and a half billion years old, and is currently about half way through its life cycle. By contrast, the human race is less than 400,000 years old; this means that our species has been around for about one one-thousandth as long as the sun has. From the perspective of our relatively brief time on earth, the sun seems to be immortal, but it's really not.
Based on standard star life histories, we believe that the sun will expand greatly in size before it runs out of fuel; so much so, in fact, that it will destroy life on earth in the process. This will not happen for a very long time yet, but it means that, if our species plans to survive, we will need to find a way to leave the sun behind long before it runs out of fuel. However many scientists believe that the environmental damage we are inflicting on the planet will put our species in danger of extinction from other causes long before the sun's life span becomes an issue for us.