It is likely that doesn't come on at a set lower pressure point but that if the system sees a large enough pressure difference between tires it will turn the warning on.

I don't know how the Volvo TPMS system is set up (my car does not have it)but the Mercedes product that I work on that has the TPMS sensors is set up so that the system can be reset/restarted for the current tire pressure to be the correct pressure and it is monitored for that pressure.

The batteries for the TPMS sensors from what I have heard/seen are supposed to be good for about ten years.