From: Maura (7/98)
On storing breastmilk: what you pump and store when your infant is 3 months is not the same milk nutritionally that you would express when the infant is 9 months. The baby has different nutritional needs as it grows, and your milk changes accordingly to facilitate the growing needs of your baby.
Also, the hind-milk, or that which is expressed last has the highest fat content, and satisfies hunger; the fore-milk, or that which comes first is thinner, with a higher water content and satisfies thirst. So if you give your 9 month old baby milk that is 6 months old you may want to consider whether she or he is: a) getting the milk that is nutritionally right for her or his age, and, b) whether you're giving enough of the fore and hind milk to satisfy both thirst and hunger.
I don't know much about the the possibility of rancidity, but I hope the above helps somewhat.