In reply to robate:
> A hang dog look in general life is a downcast, sad appearance and a downcast dog has its head hanging down with a pathetic look; works for dogging a route I think
Possibly but I feel that it all stems from the 'dogging':
"Every step Johnson took was dogged by reporters" Which conjures up images of terriers nipping at heels or even attached to trousers and having to be shaken off as well as the sense of being worried into submission by their persistent bothering of their prey.
The hanging bit is merely the facilitator of the dogged attempt