I would guess memory leak problem given that it's time dependent.http://en.wikipedia.org/wiki/Memory_leak
^Look especially at 'Effects'
This especially makes sense if the memory leak is in the kernel, as OS usually kill the task taking up the most memory when no memory is left, in this case, it would kill the OS.
Another possibility is power supply problem, this is a little more likely.
Did you replace all
of the RAM?
If so then it's probably the power supply.
Factoring in the noises however makes me rather clueless...
If it slows down before it fails then a memory leak is likely.
Other people here may know more than I do though.
I recommend asking in IRC.hackthissite.org.
Use task manager to check your memory usage over time.
If it continues to rise, try to find the task that is taking up your memory.
There is a chance that a virus is taking up all of your memory (by constantly executing itself)