You know, I wonder if this isn't a common problem? I also have a Y2 dd who struggles to finish things. She's a very strong reader with an impressive vocabulary who finds it difficult to start tasks, let alone finish them. I think she has quite low self-esteem combined with high expectations. She can't live up to herself, she's filled with self doubt but is also a perfectionist.
Yet, like others have said, once she's doing something she concentrates and focuses very well.
But what I want to know is ... do they ever grow out of it? Can you do anything to spur them into action?