I know that a lot of folks find this plant to be a nuisance, but I'm adding it to the list of tough, and at least in my eyes, worthy plants. Stachys byzantine.
I've had Stachys byzantine for at least 6 years and I've only once seen a seedling out of the beds/areas I put it in, and that was where I tossed the clippings so you'd expect some there. I love them, the bees love them, and I wouldn't want to be without them. I do cut mine back after the first heavy flowering, and thin them down a bit at the same time, then cut them back before winter...perhaps that makes the difference? At any rate, I don't have to water or add mulch to those beds; the lamb's ears cover all exposed soil in between other plants and use little water themselves.
Beginning of season...
End of season...