They come up the following year. Of course, my garden is mostly heavily mulched which I am sure really helps. I just had to pull most of the ones from past years when I was redoing beds as they were in the wrong place. They are so cheap that I don't mind buying new ones.
I used to have the regular sized glads too and they come always up the following year too. But I pulled all those and tossed them after I discovered the Glamini glads. I do so like the shorter version.