Edit after someone corrected me.
Please refer to this comment: https://news.ycombinator.com/item?id=29490291
Three of the four imagers on the telescope are passively cooled and will work as long as they don't succumb to radiation, diffusion, etc. The fourth one (MIRI) has a cryocooler that uses liquid helium, but it will leak out very slowly and mechanical wear and electronics lifespan is expected to be the limiting factor there. [0, 1]
As stated in other comments, the primary driver of lifespan is a combination of how stable the telescope orbit is, and the resulting amount of fuel needed to keep the telescope in a stable orbit. Depending on how things go it has enough fuel for somewhere between 5.5 and 40 years of operation. Assuming nothing else goes wrong. :)
"Webb is designed to have a mission lifetime of not less than 5-1/2 years after launch, with the goal of having a lifetime greater than 10 years." [2]
0: https://jwst.nasa.gov/content/about/innovations/cryocooler.h... 1: https://www.nasa.gov/feature/jpl/how-cold-can-you-go-cooler-... 2: https://jwst.nasa.gov/content/about/faqs/faq.html
At the end of the link is the clarification:
Drs. Heng and Winn respond:
As pointed out to us by Drs. Jason Kalirai and Jason Tumlinson at the Space Telescope Science Institute (STScI), as well as Mr. Sykes, our article misstated the reason for the finite lifetime of the upcoming James Webb Space Telescope. The mission duration of 5.5 to 10 years is not limited by the supply of liquid helium, as we stated. Rather, it is limited by the supply of hydrazine fuel needed to maintain the spacecraft’s orbit.
Thanks for the correction, will edit my parent reply.
Here is Dr. John Mather explaining it: https://youtu.be/4P8fKd0IVOs?t=1321
/kidding
//a little
5.5yr is the minimum, 10 sounds probable (stated goal), while 20-40yrs is the best guess with expected fuel usage.
https://space.stackexchange.com/questions/55309/james-webb-t...
I'm pretty much 100% sure NASA knows this better than me of course, but I'd love to see the reasoning behind planning to retire such an expensive project after a (relatively) short ~10 years.
2) no vehicle exists/existed at design that could support a re-fuel system.
Basically, because there is no reasonable way to service something in L2, they can't really plan for it, but it's expensive enough that they made sure there is the capability if someone in the future would, say, build a spaceship that is orbitally refuelable and designed so it can take crew that far out.
I wonder that mostly because we've managed to use a lot of our other space equipment well past their their mission lengths. I'd be interested if JWST is possibly the same.