The US military is testing stratospheric balloons that never have to come down
technologyreview.com
technologyreview.com
There are some fantastic amateur projects doing similar things, such as this 11 gram payload (!) that circumnavigated the earth 6 times: http://leobodnar.com/balloons/B-64/index.html
You fill the balloon so it has slightly positive buoyancy. As it rises, it encounters lower outside air pressure, and expands to match it. Eventually it will rise to an altitude where the pressure is so low, that the latex is stretched beyond its limits and bursts. Typically at about 40km and about 100x expansion in volume.
To prevent bursting, you need a more complex material that will expand many times at first (to allow the balloon to rise to operating height), but will then stop expanding without breaking.
https://sites.wff.nasa.gov/code820/spb_differences_between_z...
I don't see any way to make a balloon stay up forever unless you have a particle accelerator to manufacture new helium to make up for leakage...
It's not like there are any better options? The only two practical lifting gases are hydrogen and helium. Hydrogen leaks even more than helium and is flammable, even though it is much cheaper and abundant.
To counteract this, I recall reading about people trying to send balloons across the Atlantic and needing to use ballast to stabilize the altitude and handle the gas losses. I wonder how DARPA can go without this requirement, as Helium really likes to escape whatever it's trapped inside of.
These persistent, balloon based "eyes on the sky" are/were a huge difference maker in the security in Iraq, and were then transferred to Afghanistan to provide US military base security.
I don't have a link handy (I'll try to find), but I remember as attention was re-focused on Afghanistan (after Iraq) those in charge were eager to bring this successful tech to the battlefield as it offered them a 360 degree, real time tracking ability for immediate base security.
Edit: I found a link, not my source but it gives some background: https://www.nytimes.com/2012/05/13/world/asia/in-afghanistan...