It won't have been a coverage issue, it'll have been an issue of (a) where you were and (b) the fact that Doncaster isn't a LARS provider but Humberside is. Humberside provides LARS out to 30nm radius which covers as far west as Doncaster. Unless you were looking for a Doncaster zone transit or were transiting round the edge of their zone, they probably decided you weren't of interest/concern to them.
NS