They cannot die from old age.
Unless it says so on the ability, your character does not die when they reach their racial maximum age, because they do not age to reach that maximum age, their actual age is stuck at whatver age they had when their character obtained that ability.
There are very specific abilities that say they prevent that death from old age, like the ones you listed and the capstone of the Time Oracle:
Upon reaching 20th level, you become a true master of time and stop aging. You cannot be magically aged and no longer take penalties to your ability scores for aging. Age bonuses still accrue, and any aging penalties that you have already accrued remain in place. You cannot die of old age, but you can be killed or die through accident, disease, poison, or other external effects.
The book that introduced the Eternal Youth grand discovery was released earlier than the one that introduces the Time Mystery. You will notice that the wording here is different because it says you still obtain the bonuses, but not the penalties.
However, the ultimate magic also introduced the Immortality arcane discovery. So, the same book introduced two different "immortal" type effects.
Based on this observation, it is safe to assume that the rules as written are also the rules as intended. As seems to be no FAQ or errata about this either.
You will keep the penalties and bonuses if the ability says you do. For Eternal Youth and Immortality, you keep the bonuses and remove all penalties. They will also recieve no further bonuses if they obtain enough age (except if they obtain mythic immortality) as they cannot age normally anymore.
Back in 2012, when Sean K. Reynolds was still a developer at paizo, he posted agreeing that wizards with immortality could life forever. So the rules as intended, at least for wizards, seems to be that they are no longer affected by aging once they obtain the discovery.
Druids and Monks
Druids and monks are probably the oldest example of a class that does not age, with the Timeless Body ability obtained at 15th (for druids) and 17th (for monks):
After attaining 15th level, a druid no longer takes ability score penalties for aging and cannot be magically aged. Any penalties she may have already incurred, however, remain in place. Bonuses still accrue, and the druid still dies of old age when her time is up.
You will notice that the text is very similar to the one from the Time Oracle, and the reason for that is that your character gains the bonuses, but not the penalties, so they can die because they are actually aging, they simply have a body that will not suffer penalties from their age.
Keep in mind that with Wish and Limited Wish, a wizard can obtain other means of immortality that does not depend on reaching 20th level, such as duplicating the Reincarnate spell to become an adult again. Or even make Clones.