Your cells have things called Telomers that terminate the cromosomes.
These get shorter each time a cell divides until they get too short and the cell dies.
http://learn.genetics...gin/traits/telomeres/
It's thought this is a key factor to ageing - the fuse we all live with.
There are currently 12,000 people in the UK over 100
in 2011 there were 83 over 110 *in the whole world*
That should tell you that there's a biological limit.
"Fixing" that problem probably involves fixing the telomere issue but it's difficult to know what would happen if you could, as you'd be upsetting a fundamental piece of adaptation in the cell.
A bit like tinkering with a formula one engine on the basis of GCSE mechanics