There's lotsa lot of information available about how long pumped breast milk can be kept for, generally citing different temperature ranges.
From the CDC (though the samereferencesame reference is also cited by the Canadian Pediatric Society):
It's cited that milk thawed from the freezer should be used within 24 hours in the fridge, or 1 hour at room temperature.
The Mayo Clinic has an article saying "Other studies have shown that refrigeration beyond two days might reduce the bacteria-killing properties of breast milk", but no references to where this comes from or any further information.
My wife is exclusively pumping, and so there is a lot of milk cycling in and out of the fridge. She is always concerned about using milk taken out of the fridge (generally +/- 1 day old) within an hour or two. We often talk milk out (and let it warm up to room temperature), only to have baby fall back asleep. Is there a basis to how long fridge-temperature milk (stored at 3 degrees C for a day or two) can be out of the fridge for before it has to be used/tossed?