I agree. The only way for it to work is if Kagome figured how to prolong her life. One time they talked about InuYasha thinking about being a full Human.
Instead of that, they should just figure out how to make Kagome half demon.
I disagree. No, she won't live as long as he did, but what's the saying "it is better to have loved and lost than to have never loved at all"?
They're soul mates. The idea of old age being what prevents them from being together is what wouldn't make sense to me. I don't think Inuyasha would abandon Kagome just because she was old. I think at some point maybe the physical side of things would change, with him looking after her and worrying for her...but he'd still want to be by her side because it's her that he loves, not her physical appearance. I think we tend to think it does not make sense because we (and I judge not and lump myself in this category) tend to be more superficial about matters.
If you want to see where it would work, check out Highlander. In it, there is also a relationship between an Immortal and a regular human being. Despite being told to let her go, he doesn't, and I don't believe either regretted the decision. There is also an episode of Farscape, called The Locket, where a character ages, and the love she shares with another never extinguishes on either side (though they don't...to my knowledge...consummate their relationship as she has aged dramatically to the point where she might be 70 or 80 in human years). So maybe I'm just use to this sort of thing.
I guess it just boils down to a personal decision we see ourselves making. I'd rather have one lifetime of being with the person I love the most than denying that relationship (and still feeling heartbreak and now regret) because they will age/not age.
They would likely be able to age together. Early on in the series (first few episodes actually) when InuYasha is informed he has been under the spell and sealed for fifty years, and he notes that Kaede has aged (he had last seen her as a little girl), he remarks age is not something he needs to worry about, "at least for a while anyway". He may not age as fast as humans, but he is half-human. And he's not really immortal. Having said that, I agree with the previous response.. it is better to have loved and lost than not be with the one you love for something like age..the importance of superficial appearances and age kind of diminishes in the scheme of things like that. They are soulmates; of course they will be together.
And it seems Kagome only figured it out towards the end, why the well had stopped working really..it was her own feelings that blocked the way. Subconsciously she felt she couldn't put her family through that kind of hell again. So when she acknowledges that, and her overwhelming desire to be with InuYasha, the portal opens up again and she is able to return to him in his time.