I think as a chemical it's very stable when stored correctly.
It would need a very high temperature to cause chemical breakdown, 100's of degrees celsius.
It is susceptible to moisture (apparently causes clumping, same as granulated sugar would, it's not clear if this changes its chemical structure though, I think probably not).
Gradually breaks down from exposure to air, apparently, although this would take a long time.
There is a Wiki page for SN, and lots of other information online too.
The common advice is to keep it well sealed, away from moisture. The usual 'cool dark place' as for most chemicals/ medicines etc.
It is a chemically simple salt. Some reports say that if stored properly then theoretically it will never expire; its chemical makeup should easily remain stable for decades or more.
I bought SN recently, its expiry/shelf life is 3 years from the date of manufacture, both dates are on the packaging. I think this 3 year shelf life is a standard claim the manufacturers give as a quality assurance standard.
I bought 2 bottles, one I opened to check/test, one I have left unopened.
As mentioned it can be tested with aquarium strips and I understand there is also a blood test method too which is more precise. But if it looks and tastes right (be careful!), it's almost certainly fine (that's just my opinion).