Age and pregnancy loss
As a woman gets older, her risk of pregnancy loss increases, as the following graph shows.

The chance of a genetic abnormality increases with the mother's age, as the cells start to divide abnormally and distribute unequal amounts of genetic material more often.
This is one of the reasons why older women can have a more difficult time getting pregnant. When they do conceive, their pregnancies are at greater risk of miscarrying and their babies have a higher risk of genetic abnormalities, such as Down Syndrome.
Another key factor is the age of the eggs produced by the woman (and, in turn, the strength of the egg's metabolism).
Unlike men, who can make new sperm all their life, women have all their eggs from a very early stage in their development (from about 20 weeks before their own birth) and these eggs have to last them all their reproductive life. So a woman's eggs are actually as old as she is (or actually a little older!).
In every kind of cell in almost every type of living thing, energy is produced by tiny structures called mitochondria. When an egg is fertilised, the embryo receives all of its mitochondria from the mother. As the fertilized egg divides, the mitochondria don't - at least not until after the embryo has implanted and pregnancy is established.
Because an embryo's mitochondria (and ultimately the baby's mitochondria) come from the egg, the mitochondria can also get old, with the number of remaining healthy ones running out before the cells in the fetus start making new ones. If this happens, the embryo will run out of energy, resulting in an early pregnancy loss, failure of the embryo to implant, or failure of the fertilized egg to divide properly.
There are currently no routine tests available to determine if the mitochondria of eggs is in a critical state, but this is an area of active research.