Since this realies on information from False gods it's in spoiler tags. It doesn't really spoil the plot in any way, but I thought I'd be safer this way.

Horus speaks to Chief Custodian Constantin Valdor in the book, since this was the name of the Chief Custodian at the time of the Age of Apostasy I think we can finally say for certain that the Custodes don't die of old age.

Nice to have a theory you like vindicated.