Well, iron is non-renewable, copper too, every metal actually. Actually everything we mine is non-renewable.
If anything, helium is the only renewable thing we mine. Helium is just alpha particles produced continuously inside the Earth from the decay chain of uranium and thorium. It was produced for billions of years and will continue to be produced for billions more. It continuously seeps upwards. It stops where other gases are stopped, which is a way of saying you find it in reservoirs of natural gas. There are natural gas field in America yielding more than 1% helium. Helium is just not valuable enough to be worth separating it from natural gas in the majority of cases.
If the market will demand it, it will happen. For all practical purposes, helium is an infinite resource on Earth. However, at a finite price, it is a scarce resource.