Why does evolution not make our life longer?
Why do we age is a classical question in Evolutionary Biology. There are several things to consider when we think of how genes that cause disease, aging, and death to evolve.

One explanation for the evolution of aging is the mutation accumulation (MA) hypothesis. This hypothesis by P. Medawar states that mutations causing late life deleterious (damaging) effects can build up in the genome more than diseases that cause early life disease. This is because selection on late acting mutations is weaker. Mutations that cause early life disease will more severely reduce the fitness of its carrier than late acting mutations. For example, if we said in an imaginary species that all individuals cease to reproduce at 40 years old and a mutation arises that causes a fatal disease at 50 years old then selection can not remove it from the population - carriers will have as many children as those who do not have the gene. Under the mutation accumulation hypothesis it is then possible for mutations to drift through the population.

Another hypothesis which could contribute to aging is the antagonistic pleiotropy (AP) hypothesis of G.C. Williams. Pleiotropy is when genes have more than one effect, such genes tend to cause correlations between traits, height and arm length probably have many of the same genes affecting them, otherwise there would be no correlation between arm length and height (though environment and linkage can also cause these patterns)... Back to AP as an explanation for aging, if a gene improves fitness early in life, but causes late life disease it can spread through the population via selection. The favourable early effect spreads well because of selection and, just as with MA, selection can not "see" the late acting disease.

Under both MA and AP the key point is that selection is less efficient at removing late acting deleterious mutations, and they may spread more rapidly thanks to beneficial early life effects. Also if there is extrinsic mortality (predation etc.) then the effect of selection is also weakened on alleles that affect late life. The same late-life reduction in the efficacy of selection also slows the rate at which alleles increasing lifespan spread.

A third consideration is the disposable-soma model, a description by T. Kirkwood of life-history trade-offs which might explain why aging and earlier death could be favoured. The idea is that individuals have a limited amount of resources available to them - perhaps because of environmental constraints or ability to acquire/allocate the resources. If we then assume that individuals have to use their energy for two things, staying alive via repair and maintenance (somatic-maintenance) and making offspring (reproductive-investment), then any energy devoted to one will take away from the other. If an individual carries a gene that makes it devote all of its energy to somatic maintenance then its fitness will be very low (probably 0!) and that gene will not spread. If the level of maintenance required to live forever costs more energy than an individual can spare without suffering from low fitness (very likely) or can even acquire and efficiently convert in the first place (also very likely) then high-maintenance alleles will not spread (and aging &amp; death will continue to occur). 

To go a little further, it is common for sexes to age differently (this is what I work on) and one possible explanation is that the sexes favour different balances of the trade off between somatic-maintenance and reproductive investment, this can lead to conflict over the evolution of genes affecting this balance and slow the rates of evolution to sex specific optima. This paper provides a good review of the area.

To summarise, evolution has not managed to get rid of death via genetic disease etc. (intrinsic mortality) because the effect is only weakly selected against, and those alleles may provide some early life benefit, and resource limitation may also reduce the potential to increase lifespan due to trade-offs with reproductive effort. Adaptive evolution is not about the survival of the fittest but the reproduction of the fittest - the fittest allele is the one which spreads the most effectively.

EDIT: Thanks to Remi.b for also pointing out some other considerations. 

Another thought is that of altruistic aging - aging for the good of the population (the population is likely to contain related individuals, you are related to all other humans to some degree). In this model aging is an adaptive process (unlike in MA where it is just a consequence of weak selection). By dying an individual makes space for it's offspring/relatives to survive (because resources are then less likely to limit populations). This will stop excessive population growth which could lead to crashes in the population and so, by dying earlier, an individual promotes the likelihood that its progeny will survive. Arguments of altruistic sacrifice are often hard to promote but recent work suggests that this is a more plausible model than once thought.

Evolvabilty theories also suggest that aging is an adaptive process. These suggest that populations, composed of a mixture of young and old, have biases in how well adapted the members of the population are - where younger individuals are better adapted (because they were produced more recently it is likely that the environment is similar to the environment they are favoured in). Thus by removing the less well adapted individuals from a population via senescence and freeing up resources for younger better adapted individuals, a population evolves more rapidly towards it optimal state.