Oh look, it's this thread again. Not like we had one thirty minutes ago or anything.
Here we go again:
Time travel in Samurai jack seems to function on a single, dynamic timeline, where travelers can move forward and backward freely.
However, it seems that travelers have a fixed position in time in which they are intended to exist, and thus are tied to that point no matter when they travel to.
When Jack was flung forward, the timeline continued with Aku's reign and Jack's absence, and we got the future seen in the majority of the series. But Jack himself was displaced in time, meaning he stopped aging as soon as he left the point in time he belonged in.
So basically, for the entirety of the series, up until Jack got back to the past, he wasn't aging because his own time was still rooted in the past.
Ashi, on the other hand, was born in the Aku future, and so her existence was tied to it. When her and Jack went back and destroyed Aku, the timeline was altered from that point on, meaning no Aku and Jack starts aging again.
Altering the timeline wouldn't necessarily erase everyone from the future, and I think there's a good chance many of them went on to be born regardless. Ashi though was tied to Aku's existence, which is why she disappeared when the paradox caught up to her "Back to the Future"-style.
I don't know why I bothered to type all this out, but whatever. People are still going to complain.