'keep digging' refers to when someone has just said something embarrasing or awkward and they are trying to get themselves out the situation by backpeddaling but they are just making the situation worse.
for related topic see dig a hole pass me a shovel and ground swallow me up
Frank: Hey when's the baby due?
Mary: I'm not pregnant.
Frank: Of course you're not...errr...you look really good
Mary: You're digging a hole
Frank: Uh-huh oh by the way did I forget to mention your hair looks nice
Mary: yeah? keep digging!
Frank: Ok I'll see you round...I mean around.