I look after my baby sister while my mom works at night. She pumps milk, but will sometimes leave it out at room temperature for an hour or two before putting it in the fridge-she forgets about it. Is this dangerous?

Nope, that's fine. Breastmilk can be left out for up to 6 hours before use. As long as it's getting used within the next day or two it will be fine.

It always gets used up pretty quickly because there isn't much stored-mom never much built up a supply to keep when she started working again. Why is that ok when cow milk has to be refrigerated?

I figure there is something in cow milk that ends up going stale quicker than brest milk would. That is only a guess though and Im not really sure but would love to know if someone out there does know.

Here's the time lines I found online:

At room temperature (less than 77°F) for 4 to 8 hours
At the back of a refrigerator for 3 to 8 days
At the back of a freezer for up to 3 months(http://familydoctor.org/online/famdocen/home/women/pregnancy/birth/828.html)

There doesn't seem to be any information as to why it is so stable at room temperature compared to cow milk or other types of milk though.

Well thanks, it's reassuring to know that we aren't poisoning her, and that we don't have to throw away the milk if mom falls asleep! It's proving hard getting a little stash going, because she went back to work so fast.

Breast milk can be left out longer because it is "alive". There are living cells and antibodies in breast milk that keep it from going bad. Cow's milk has been pasteurized, which kills the germs, but also kills all the good stuff that keeps the milk from going sour.

Exactly. This is how breast milk supports and primes your baby's immune system. Your milk contains good bacteria and immune factors, and the good bacteria colonises your child's tummy. Formula fed infants miss out on this.