Q:

Should a user lose her reputation from a closed question?

As it is mentioned numerous times, there are question on Stack Overflow that are there just for historical reason, showing "What we should not do/ask". Most of these questions are closed as off-topic, not constructive, too broad, etc. In addition, most of these questions show minimal to no effort.
The argument/question here is: Why should the user retain the reputation and (maybe) the badges earned for this question?
Another issue which again was discussed many times is that this type of questions is a bad example for new users. Having or showing the positive votes on closed question may be mislead the new users, thinking that this question is great, even if it is closed.

A:

Why should the user retain the reputation and (maybe) the badges earned for this question.

We (as a community) have changed our views over time about what kind of questions are acceptable.
That shouldn't mean that we retrospectively punish users for posting a question that was acceptable at the time it was originally posted.

A:

Why should the user retain the reputation and (maybe) the badges earned for this question.

Because enough users thought their post was helpful, and that is enough reason for it. We don't scrutinize user's voting choices as long as it's not serial or sock puppetry.

In addition most of this questions show minimal to none effort.

If they are highly upvoted, obviously a lot of people disagree with you on that.

Another issue which again discussed many times is that these types of questions are a bad example for new user.

That's exactly why we have the big yellow box telling new users not to post stuff like that. We expect new users to be able to read.

