A doctor in charge of a blood extraction campaign explained to me that this is exactly the reason why there is a constant high demand of blood donors. Between hospitals there are exchanges daily of blood (you might have a certain blood type that another hospital needs right now), but a lot of blood does get wasted, because of the short times it has.

They also separate blood in different kinds (platelets I think it was the term) since it can be storaged for longer, but is not as useful as a full blood transfer.