They die... for a while at least
Those Rubric Marines are indeed nothing more than a spirit animating armor, which makes them tougher than average Space Marine (i.e. they can't be poisoned) but they are still far cry to the toughness of Plague Marines for example - suffering enough damage they will "die".There is also nowhere mentioning about reattaching amputated limbs, so one can assume that severing the armor's arm you also sever the spirit inside it.
But on the plus side, they can't be killed permanently: the same spell that created them can be used again to revive/repair them to the original form. Unfortunately such a spell is difficult and time consuming, so it cannot be used in the heat of battle.
In editions past it was mentioned, that Thousand Sons Sorcerers can reanimate killed (broken?) Rubric Marines with a simple yet time-consuming ritual and Magnus himself can somehow bring back fallen Sorcerers in his super-awesome Black Tower on the Sorcerers Planet. All of this was possible because Rubric made the souls of both Golems and Sorcerers all but immune to powers of the Warp so they cannot be nommed by daemons - although as Erebus had shown in "Betrayer", it is quite possible (though not easy) to resurrect even one who's soul had being torn apart and eaten by daemons. It was never retconned, so we can assume that this fluff is still valid, and no matter how many Thousand Sons you've killed, they would always come back from the dead. At least they wouldn't do it right the next second after you've killed them.