I had a turtlehead in my garden for about 6 years. Odd thing -- it kept thrusting itself up above the garden surface. I was always adding soil and mulch to cover the roots. I have a sprinkler system, so it got enough water. I had the same problem with agastache Blue Fortune. Every autumn I made sure to cover the plant roots all snug as a bug in a rug with mulch and soil and every spring I would find it nearly thrust completely out of the ground.
The turtlehead lasted longer than the Blue Fortunes. But alas, one year the turtlehead totally thrust itself out of the ground and came back no more.