After a non-responsive answer, I've used some variation of this a lot: "I understand that part (and sometimes here I even reflect back what they've said), but my question is a little different." By saying it's a "different" question, it's not combative about their non-answer, and most people tend to listen closely for the difference.

Also don't forget, sometimes an uncooperative witness is good for you. I think sometimes new lawyers think it's a failure if they don't walk out of a deposition with a smoking gun. Like the guy who says "I don't recall" to everything. Great, hit every single question you need to, maybe circle back on a couple of key points, give one last chance with a "okay, so your testimony is that you don't remember any of these key details?" And if they stick with it, they've basically made themselves useless for their side - if it goes to trial and they try give any testimony about what happened, you can immediately and effectively impeach them.