How should I ask a potential advisor why they haven't published in the last 3 years?
Instead of a question that might be insulting, you should probably ask them what they've been working on for the past few years. You need to know that in any case and their answer might give you the reason that they haven't got anything out recently. There may be a lot of work in progress but not yet ready. That sort of thing can actually be an advantage to you and knowing what it is, certainly is.
But if their answer indicates not much research, then you might want to keep looking.
By the way, this is a topic for a sit down conversation, not just an email. The latter might work, but would require more work from the prof and so you might not get as complete an answer.
I think in a very real sense, you are, in fact, interviewing potential advisers. It would be rather disingenuous for a potential adviser to believe that he or she is beyond the bounds of accountability for his/her research record. I would say something such as the following:
I am interested in participating in publishing papers. Would we be able to publish papers together?
What types of projects/papers have you worked on in the last few years?
What are some of the current papers or projects you are working on?
A quality adviser would have quality answers for these questions. Moreover, they would know that it would play in their favor to have at least some explanation as to why they have not published lately. These questions will open the door for them to provide an explanation of their research record. If they seem to dodge around that time period, I'm honestly not sure that they should be your number one choice for an adviser.
I would also verify that this is not just a matter of their CV being out of date. Perhaps they have published papers and just have not updated their CV in a while.
Aside: If I can give my personal thoughts on choosing a young, unproven adviser, I would recommend avoiding professors who have not established themselves somewhat. I have seen a number of PhD students who run into issues when they choose a professor who has not yet been given tenure and who is constrained by the "publish or perish" mentality.
Given the publish or perish mentality, a (young) researcher that "has published...nothing for the last 3 years" is heading towards perishing, at least, they are in many disciplines.*
Although I agree with Buffy that "[they] may [have] a lot of work in progress but not yet ready" and that "sit down conversation, not just an email" is most appropriate, I feel that nothing for three years is simply too long and it doesn't give much confidence that they can help you churn out publications (to get a PhD).
I recommend rethinking their suitability as a supervisor.
*As noted in the comments, established researchers (or researchers with protected employment statuses) enjoy more freedom.
I'm not an advocate of the publish or perish mentality, but that's the world we live in.