All routers are in the same AS, so these are iBGP peerings. In iBGP, routes learned from one iBGP neighbor are not advertised to another iBGP neighbor unless route reflection or a full mesh is used. Configuring the central router as a route reflector with the ASBRs as route-reflector clients allows routes learned from one ASBR to be reflected to the others, restoring route propagation between them.