Going from memory and what I remember from my combustion class.
The strange thing about diesels is that their A/F ratio varies from idle to full load. If you look at what happens: The same amount of air (minus induction efficiency at given RPM) is induced into the cylinder at every intake stroke. The fuel is then injected into the air charge. At idle a small amount of fuel is injected and at full load the maximum amount of fuel is injected. The maximum ammount of fuel is designed based on a "fresh" engine. Once the engine gets "tired" it will flow less air, have a higher leak down rate in the cylinder or have a slightly smaller compression ration due to wear ( not much though). All these factor add up and the engine ends up with less air for a given amount of fuel, assuming the amount of fuel does not change.
As the engine gets older the the cylinder produces a lower pressure. Combustion efficiency is based in part on the air pressure, and thus heat, in the cylinder. As the pressure falls less fuel can be burn completely.
Another factor can be carbon build up in the head or worn injectors. This can cause the fuel to pool up into large droplets. These large droplets will not burn completely in the amount of time that the combusion has to finish.
Again, this is from the top of my head.