So I was Sharding the Shard when I read a topic concerning the Boons/Banes and realised that the immortality of the Heralds sounds like a Nightwatcher "gift".
-They never die but, have to endure incredible pain.
Another reason I have for suspecting this is the Knights Radiant. The spren fashioned themselves after the Honorblades and Heralds. They not only grant Surges but, also physical ability, as seen with Kaladin. However there is no mention of Knights having longer lifespans or going to Damnation every so often. This is why I think the ability isn't from Honor ,but from a different source (aka Nightwatcher).