espo, bad news for some.
Yes and it also doesn't last.
So, if the heat treat and re-arch is done to the same level as the original spring forming it SHOULD last just as long as it did originally. The metal shouldn't care if it's the first time or not if it has truly been "reset" appropriately.
Now, having said that, if the re-arch and following heat treatment isn't taken to the necessary level (time, heat, re-arch spec, etc), then you are correct, it will not last as long.
Ultimately, it depends on the spring shop doing the work.