Do organ donor centers keep a big file of everyones histocompatability information?

Yes - stored forever: Histocompatibility information about each donor and recipient is permanently stored at each transplant center and at unos (united network for organ sharing). Although the person's "tissue typing" never actually changes, techniques improve over time. This may lead to new identification, or change in the naming of the tissue type (although the tissue itself remained constant). Updating may be needed.