Telomerase comments

 Many species of protozoans do not express telomerase during mitosis (but only during conjugation), so their telomeres shorten with each reproduction, leading to a limit of a few hundred reproductions per cell line.  This mechanism is the precursor to telomeric aging that exists to the present day in humans and many other higher animals. ...

Therefore, any cell lineage that does not conjugate will die out after a few hundred generations. This prevents cell colonies from becoming too homogeneous. -link

Snippet from a post josh mitteldorf's blog. The article delves on the promising science of telomerase and its underfunding. I agree that telomerase research should be better funded and sounds quite promising.  I too agree that the need for genetic diversity may be a reason for the existence of an aging process.

Genes that promote variability or diversity in a population will be more likely to be successful than those that don't.  In the absence of aging, populations are subject to the older organisms competing with the younger less mature ones for limited resources and the fittest organisms would be the least likeliest to die in a population barring aging.

EDIT

Reply from topic

 "Josh, yes telomeres are an ancient clock, the even occur in paramecial macronuclear DNA – but there -they don’t shorten. So that’s paramecia, they’re weird in any case – but the same is true of mice – their telomeres don’t shorten with aging – and in case the readership doesn’t know, mice last two to three years (I’ve heard of four)."-Harold Katcher

Mice have other reasons for being short lived.  In fact some say they die mostly from cancer so their long telomeres and telomerase may be a mechanism to cause them to die on time . 

"Anyway the important thing is to get to the cause of aging – attack each arm of the octopus or hydra; amyloid accumulation, DNA damage accumulation, lipofuscin accumulation, ROS production, mitochondrial dysfunction etc."-Harold Katcher

We would have to look at what exactly is being implemented in negligible senescence organisms to see if all of those need to be addressed.  

We know that even smoking 60 cigarettes a day which should surely increase all forms of damage, doesn't impede a human from reaching 100 in good health.

We also know that mechanisms must already exist or be present that allow one of the most metabolically active cells in mammals to live extraordinary long lives far in excess of pretty much any other cells.  Neurons live over a century in humans, in other mammals transplant of neurons showed they could live twice as long as original host without genetic modification, it may be the case that human neurons too could live twice as long for all we know.   What changes needed implementation to go from 2-3 years to 120+ years in neurons within mammals?
  That would be interesting to know.

One might say lots of changes or things had to be addressed, but the cells from shorter lived rodents were transplanted unmodified and exceeded twice the lifespan of the original host organism.   IF there truly was a serious change needed, at least in these cells, one wouldn't expect them to live twice as long as the host(and it is believed they could've lived even longer).without necessary modification.