Could you elaborate a bit on the whole "tethering" thing? I'm new here so please excuse me if I'm missing something obvious - are you talking about tethering to the ground or something else?
If it's the former, I'd be curious what material you'd be using to get up 15,000+ feet while still tied off.
As to the properties of a latex balloon, I bought a bunch of 200g balloons just for fun and testing. Sent one of them filled to about 4 feet wide up on 100ft of parachute cord above my house so my friends could follow it to my place for the reveal part for our footage. It was up there for a day, and then it shrank to about 3 feet and lost a lot of buoyancy, so I kept it inside another day. On the third day I tried to fill it back up and after only a few cubic feet of inflation, it burst.
I noticed some distorted patches on it just before I tried to refill and had a feeling it might not take it, but tried it anyway - all in the name of science of course.
Anyway, I wouldn't bother trying to reuse, or if you do, use a new balloon each time and use the helium left in the previous one to begin inflation of the new one.