I'm not pretending to be an expert but the question intrigued me so I tried to come up with an answer. You might have to wait until after New Year for a clued-up MN expert to see this and reply.
I think this is a common myth for breastfed toddlers, that there are no immunological benefits. Keep in mind we are not cows, to start with.
Had a quick look on Internet and the sources I've found on the Internet say 24 hours for calves, puppies, kittens or piglets and absorption of colostrum immunoglobins (not 8 hrs).
This page talks about early milk immunoglobin absorption for different mammals, making it clear that ruminants are quite different from say, rats (20 days of absorption) or people. Also, there are different concentrations of various types of immunoglobins in different types of mammalian milk, and some of these can beneficial just via the mouth or stomach membranes, alone. IgA and IgG in breast milk counteract bacteria in the mouth and lactoferrin actually kills streptococcus mutans, regardless of the age of recipient (see ref).
Another thing, ruminants start eating grass typically by 2 weeks of age, whereas baby people need to be something like 10x older to be ready for non-milk food, so we would expect human milk to be more specialised and complete.... Plus people live at such high densities and intense social interaction that we have probably evolved quite differently in terms of what our immune systems need to cope with.
I'm also guessing that the types of antibody molecules in mature milk are different from colostrum (not as many, but smaller molecules). Also, that they are in there at all may mean something -- they wouldn't be there if they didn't tend to benefit the offspring. Most importantly, we know that the longer they're breastfed, babies and toddlers get the fewer colds, and they generally get milder versions of whatever illnesses mother might have (like a cold), so that's epidmeological evidence that at least some antibodies get thru somehow long after the newborn period.