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That is one determined plant! How deep are the roots the suckers are growing from? If they are shallow, you can discourage the roots by robbing them of their food supply. Pull the suckers (don't cut, pull) off the root.
Or, a second, slightly more dangerous but quicker method is cut the stems down to a couple inches and pick off any remaining leaves. Carefully paint the remaining stem with full strength brush killer. Don't get any on the soil as it will kill other sensitive plants it comes into contact with (ie: Maple trees). Using brush killer on perennials always works best in the fall as the leaves start to yellow.
Daisy