Os...I can't say I've ever had that problem, even when working with .005" "wire". When I punch in the design, I make sure to overlap each cut by as much as half the width of the cutter. That keeps lines flowing smoothly. I use Jim's technique, too, when the ribbon wants to "collapse" in on a curve. It actually stretches the ribbon so that it will go straight into the cut rather that fold over, or make a flat spot in a curve.
I've seen some wire inlay recently that does not flow as well as I'm sure the artist intended, and I have seen dark "gaps" in places along the inlay. Be sure your chisel is as fine as it can be, so that when the wood is wet to swell it, it closes the cut completely. Also, dress the wood down completely to eliminate the impression of the wire being below the wood's surface.