Thermal compound does eventually expire and go bad.
However if you keep the thermal compound properly sealed and stored in a cool dry place then the thermal compound can easily last up to 15 years.
After 15 years then the thermal compound may not be good enough to use and may harden up but usually you'll use the thermal compound long before 15 years have passed.
I've never kept any thermal compound longer than a year or so because I only buy new thermal compound when I need to use it and do not keep a bunch of it at home.
You can buy some extra thermal compound and keep it stored in your home, office etc and use it when needed but I would recommend using it up before 10 or 15 years so that it doesn't dry out and become useless.