Undergraduates have several-month long "sabbaticals" every years. While graduate students shouldn't expect to have the same thing, could it maybe be justifiable for them to take a several-month long sabbatical in the middle of graduate school? These things can be really helpful for things like evaluating whether or not you're trying too hard to reach a dead end.
We encourage our graduate students to take internships for 3 months during summer (at Microsoft Redmond and MSR Cambridge). This is a bit like a sabbatical. In our experience, these are extremely valuable for the students and for fostering research collaborations. Usually one publication results for the student, but the experience and the contacts they gain cannot be measure in the regular units.
We do not allow our students to go on such 'sabbaticals' if they are not already performing well. The lucky students who do get to go need to act as ambassadors for our university. We do not use internships as a way of kick-stacking the research of a student-gone-astray.
Unless by sabbatical, you mean vacation, in which case, I've answered the wrong question. Students are entitled to 6 weeks vacation per year (not including Christmas). They may take it in one chunk if they wish. Whether we allow it depends on what project deadlines need to be met and so forth. Generally, we encourage them to split up their vacation into smaller chunks (1 week here, 2 weeks there).
From my experience, academic sabbaticals have a direct, stated purpose; for example, performing research (and having some fun) in a different country with a different academic environment, casting your hand at doing some work in a completely different field, taking a break from work to write a few long review papers. To this end, I'm not sure what a student would do on a sabbatical; most graduate students have a single project, and they haven't been involved in research to be able to try something else–they're still learning their first field, for goodness sake. I'm not sure how anyone would benefit from a student taking a sabbatical. On the other hand, there are numerous downsides, the main one being that there is a definite chance that the student will not return to their research after doing something else for a few months. I can't think of any reason why this could be a good idea.