Limits on one student using all of one's office hours?

I will argue that setting limits for a particular student is acceptable and in some cases necessary. It really is an abuse of office hours if one student is taking up all of them, every day. Let's say that proper usage is around 10-15 min for a particular question or issue. For a particularly weak student like this I may assert, "Let's say we have 20 minutes for this." Require that she ask about a particular homework exercise that she can show prior work for. Do not just regurgitate the lecture wholesale.

By default, students should be able to master the material via lectures, study, and homework, without constant additional hand-holding by the instructor. Part of the unfairness here arises from the fact that the student is effectively getting double face-time with the instructor, relative to other students; so the one student's success does not really represent the same level of proficiency as shown by other students. Some other students may possibly take note of this, and either avoid office-hours interactions (which would be more fruitful) because of the always-present student, or silently resent the double-attention.

If the instructor (like me) is becoming physically and emotionally drained by these constant interactions, then we should learn to be sensitive to that, and take that as a signal that some change or boundary needs to get set, lest we become burned out. There is, in addition, a possibility that the student thinks they are socially flattering or flirting with the professor for a better grade. It's probably a good idea to document these interactions, in case the needy student (or anyone else) is prone to complain later about their grade or some other matter.

Under the "honesty is the best policy" principle, it's probably good in theory to have a frank discussion of expectations for the course with the student around the second or third time this happens. (But: I don't think I've successfully executed that to date.)

The real tough case for me is a student who officially meets all the prerequisites to the course and points to the first day's lecture notes and says something like, "I have no idea what any of these words mean." Perhaps they got through all their prior courses in a state of acclimation to exactly this level of double-hand-holding.

(This answer largely restates my answer and comments on that issue from this question. Thanks to the commentators there for refining my thinking on the issue, and thanks to @scaaahu for suggesting I write them up as an answer here.)

The issue here is not what proportion of the published office hours are being used by one individual, it's that "they apparently have no capacity or confidence to follow along in class, read the book, or make connections on their own."

You are this student's teacher. That gives you a special responsibility, not only to help the student master the material in your course, but also to assist in, and insist on, an improvement of his or her study skills. You are not obligated, however, to be his or her personal homework tutor.

Do not hesitate to make your expectations for independent work clear; of course, you should also be realistic, and start wherever the student currently is, in terms of study skills and ability to work independently.

Example:

Mr./Ms. X, I'm going to circle three things from the notes I made during our study session today, that I want you to follow up on, on your own. Let's review those now to make sure they're clear to you. Explain the three things to me now. (E.g. look up Topic A in the index, take notes on what the text has to say on that topic; go over the section of the textbook that was assigned in class this morning, and write an outline of that material, and highlight the parts that you were already familiar with, if any; in advance of our next class section, write down three things you want to get out of the lecture, and then highlight any parts of your class notes that address any of those three things. I just made this up, your assignment could be completely different, of course.)

You may at this point politely and cheerfully show your student the door, even if it's only been a five-minute conversation. Example:

Okay, that should get you unstuck. I look forward to seeing your progress with this assignment! I am going down the hall to do some xeroxing. May I give you a hand with your bookbag?

It is your job to make sure that you are bringing your student up, and that your student is not bringing you down.

Additional note: find out what homework help labs exist and make sure your student knows about them.