Asking for a deposit from a repeat client after previous late payments

A repeat client eventually pays every invoice, but the last three were several weeks late. Now they want another project and are surprised I'm asking for a deposit. I value the relationship and don't want to make the conversation personal. My draft explanation is that I use the same upfront payment terms for projects of this size, with milestones for the remainder. Does that sound reasonable, or should I be more direct that payment history is why the terms changed?