Eh, my post is not only ungrammatical (:-/) but also illogical...
A better word in place of "interest" would be "care". They're interchangable in Polish in such contexts... Maybe I'll just try to say clearly how I understand the idiom.
I think "to die on the vine" means to be wasted due to lack of care. I think the word "wasted" in my definition implies the potential of what dies on the vine. I also think things and processes can die on the vine even at the final stages of their production/development/course etc.
Would you agree?
PS: A word of explanation. Why do I think the lack of care is important here? It isn't explicit but that's what the history tells me. Leaving grapes to wither on the vine was (and maybe still is) considered a serious sin and people said things like this to accuse other people.