However even if we did somehow run out of Helium entirely, once SpaceX switches to Methane fuel (as they plan to do for the ITS) they won't need it anymore. Currently it's used to pressurize the tanks, but Methane does that for itself. It would mean speeding up development of 'small' methane launch vehicles presumably, but that's it.
Per the other comment, no other noble gas has a low enough boiling point to remain a gas at LOX temperatures...
And given that the nearest natural source of helium is Jupiter, that is a little concerning.
An estimated 54 billion cubic feet (1.5×109 m3) of helium was detected in Tanzania in 2016
https://en.wikipedia.org/wiki/Helium#Modern_extraction_and_d...
We already rely on nuclear reactors to get several elements that are used in radiotherapy. IIRC there was a major shortage of medical isotopes a few years ago when a Canadian reactor that used to supply most of them was shut down.
Of course, it will be expensive, so no more cheap helium balloons for our grandkids. For specialized applications, though, we can afford some artificial helium.
Sun is closer and produces helium all the time, but less practical to harvest it from.