Not sure what you mean by "shrubby perennial". It looks like Leptdermis oblonga, but this is a woody plant, although summer growth looks somewhat herbaceous (non-woody). Even in my much harsher zone 4 climate, it never dies back totally to the ground. Some years it dies back to within an inch of the surface, and it does also re-sprout from underground, but there is always growth from at least some wood from the previous year.
Now if you treat it as a perennial and just cut it back anyway, that's a different story, and you've probably never noticed that it doesn't die back so much. I suspect that in your much warmer climate, Leptodermis often won't die back at all.
