If evolution has not done it up until now, there must be a reason behind it, a reason so important that it prevents lifespans from exceeding a certain duration.
I doubt it. It took only a few million years for us to double our lifespans relative to chimps, and that was with several close calls with extinction applying selection pressures for just about everything except low intrinsic mortality.
Lack of adequate selective pressure for—and/or presense of a strong selective pressure against—longevity seems to be the problem. Evolvability, if tied to somatic mutation rates, would be a simple reason why we don't live longer. Dozens of other ideas come to mind.
Evolution may be bound by the pressures involved, to not have evolved beyond a certain degree of longevity. But that's no reason to assume that simple tweaks can't get us further. They might expose us to more extrinsic mortality risks in a "natural" environment, but we're long past that stage now.
One example is inflammation, which may serve a purpose in preventing/fighting infections, etc., a problem which we face much more rarely today than in millenia past. Reduced inflammation can allow increased longevity, via reduced crosslinking, etc. I suspect that dozens of such selection pressures and tradeoffs have been tilting in favor of longevity with each successive generation, for the last couple centuries or more.
I doubt it's so much a case of people with extreme longevity genes having a breeding advantage, as much as it's simply a lack of weeding out people who might otherwise have high longevity but would be killed before reaching reproductive age, or before they can raise their families. So I doubt humanity's new lifestyle is selecting for longevity, it's just not selecting against it as much anymore.
By not selecting for longevity, what I'm getting at is, what advantage to one's offspring would be provided by living to 100 or 110, when reproductive capacity ended 40-60 years before? Does my grandmother still affect my success, or my children's success? And she's only in her early 70's. What affect on one's great great grandchildren can one provide that would be a strong selection pressure? On the other hand, if such people face higher mortality rates before age 20, even if only 1% higher, that would be more than adequate to weed such genes out of the gene pool. Remove those pressures (which we probably have in some cases), and longevity will increase. Slowly perhaps, but it will happen, and faster than the millions of years it took to double our lifespans from that of chimps.
But, how do we do it in one generation? Biotech. Nanotech if necessary. Hmm, I'm getting a bit off-topic.
The point is, I doubt repair rates are enough, even at age 10, to sustain us much past 100 years. We need to do even better than that!
And more importantly, the point is, I don't think aging is just loss of repair capacity. The repair capacity was never there to begin with! Damage accumulates. That's aging. Loss of repair capacity accelerates the process, but even with non-diminishing repair capacity, we'd still age, and develop pathologies. We'd look young, but die of cancer, or heart disease, just as children do today, but at the rates of the elderly.
Sure, we might get a couple more decades, maybe three or four or five if we're lucky. But we need to improve the repair rates even more to live longer. That, and/or clean up accumulating damage. But since that seems a bit ambitious for an entire population of hundreds of millions or billions, improving repair rates seems as important as cleaning up the accumulating damage, at least in the short run.