There is no reason why a CPU should fail like that; look at the PC world, servers are on 24/7 without 'breaking' because their CPU mystically fails due to a solar flare on Sirius A. The Cell is just another CPU, same as every other CPU on the planet - they don't generally break once they've been tested in the plant unless you do something stupid to them (putting the wrong voltage through, incorrectly seating them, ...).
They're hardly immortal. There is a failure curve associated with CPUs, just as there are with other manufactured goods.
CPUs do fail, though they rarely fail within the expected lifetime of the chip (I think desktop CPUs are given less than a decade for their mean time before failure).
It helps that most consumers don't buy the thousands of CPUs needed to get a statistical grasp of the failure rate, nor does anyone actually run them for the decades needed for a good fix on the actual life span.
Big purchasers probably do have a better idea of the number of failed CPUs, and the manufacturers have warranty hotlines for more than overclockers and bad home builders.
It's a worsening problem as process geometries shrink, clock speeds climb, and power budgets swell.
Tiny, thin wires and transistors do not stand up forever to the pull of current flow and increasing temperature.
Small defects tend to magnify over time, even if the chip is well taken care of.
All chips will fail after a long time of thermal cycling and electromigration, we just don't usually keep them that long. However, they don't always fail spectacularly. A chip can go bad long before it stops working, it may just silently corrupt data or produce bad results in one out of a trillion cycles in one out of ten trillion inputs. A consumer would probably never notice.
There are big-tin servers that are a lot more picky, and they do see a much higher number of reject CPUs than a desktop would.