My grammar book says
"She has been promising to come for weeks."

Why does it use _ing form with stative verb?

Question

My grammar book says 
"She has been promising to come for weeks."

Why does it use _ing form with stative verb?

Answer

She has promised on repeated occasions.

Answer

To emphasize that a situation is temporary or that something has happened around the time we speak, the present, is what Cambridge says. 
Think about the McDonald's commercial or slogan 'I'm loving it.' 
Cheers!