I'd say RYTX is probably right. The reason DNA ages, is because every time the DNA molecule divides, it has to lose a little bit of DNA off of the ends. Well, it is true that the DNA in the body of a creature is constantly dividing as new cells are being formed; so some negligible amount of aging would happen while the Animorphs are morphed. However, each morph is based on a DNA 'master copy' that is absorbed directly from the acquired creature, and, since that copy is preserved in stasis in the bloodstream (that was #18 that Ax mentioned that, btw) it never divides and thus should never age, at least when not in morph. And I see no reason why that master copy should ever be replaced with the degraded DNA that's left over from the cells during the time spent in morph, which leaves out the idea of in-morph aging carrying over to the next morph. Unless the Andalites were completely stupid when they designed the technology, which, I guess, can't be completely ruled out.
By the way, fun fact: for some reason that science doesn't completely understand, lobsters do not appear to 'age.' They get bigger as they get older, but their bodies don't 'wear out' with age as other species do. It's thought that if you could keep a lobster free of diseases and predators, it would be immortal.
. . . So, if the Animorphs want to live forever, I think it's pretty obvious what they'd need to do.