It's been years since I played the Sims, but I could've sworn there was a setting where people would age up to Adult, but not any further. I certainly don't remember any people dying of old age in my games, but maybe I just didn't play any single game long enough. Also, can't you give someone a birthday cake to age them, even if you have time-based aging turned off?
In this game, several days is nothing. One of the biggest problems with this game's event system is that, if an event doesn't come up, there's no way to know whether it's because you haven't done a necessary prerequisite for the event to trigger, or because it just hasn't been randomly selected from the list of possible events. But I would at least give it a week or two before you really start to worry.