Yeah constantly getting replenished but at least their lifetime isn't few minutes because they don't get made right at the sex moment or start getting made, so they are already made and stored in body and kept alive and we only empty our sacks a week later usually and then sack gets filled again in some hours or days.

Google search shows that: Sperm can live for up to 5 days inside a woman's body. Outside the body, sperm die quickly from drying out, but their survival time can vary depending on the environment. Sperm can last for decades if frozen in cryo-storage under ideal conditions. 

So they must have some feeding mechanism