Well, anyone reading this now will most probably die within the next 80 years. It's not that much really...on an astronomical scale.
Seriously, I expect there are people alive today who will still be alive in 1000 years.
Damage in Mitochondrial DNA might be a difficult problem. Replacing the function with nuclear DNA may not be an option in cells like nerve cells, which can be very long on cellular scales.
Cancer may be an insurmountable problem. Cancer is not a singular disease. It's more of a consequence of the laws governing evolution. However, if the problem were reduced to just cancer, we would still achieve considerable life extension. (Ending with a very bad disease.)
The trend supports them, somewhat. Lifetimes centuries ago were 30-40 years on average. Only a handful of people lived 60 or more years. Today, many people live to 100, many more to 80... so we are getting better at preventing death.
At some point, if this trend continues, we'll be almost perfect at it.
The average in previous centuries was heavily skewed by infant/childhood mortality. Plenty of people lived into their 80's back then. It's just that half of their brothers and sisters died before age 10, which dragged the average down. Still more succumbed to disease and infection before even middle age.
The average isn't going up because people live longer, it's going up because fewer people die young.