The spell itself is instantaneous, and no longer exists as such after taking effect. The effect itself — in this case, continuous
confusion — is persistent, however. This means that the confusion will apply any time the target is subject to a mind-affecting effect. (I hope that made sense.)
Note that a change in the subject's status or form doesn't remove existing spell effects. If someone is under the effects of an
enlarge person spell, then gets
polymorphed into a sheepdog, the
enlarge person isn't removed or dispelled: it just no longer affects the target, because they're no longer humanoid. If you successfully dispel the
polymorph effect while leaving the
enlarge person spell intact, they will change back into their original form, albeit twice as tall.
The PDF
Portable Hole Full of Beer (This Product Contains No Alcohol) included a 'dead' template, which if applied to any creature turned it into a dead version of that creature. While it wasn't supposed to be taken seriously, they
did accurately reflect the rules, and it never stated that ongoing spell effects were removed.
(Incidentally, that PDF has been updated with a sequel, now titled
Bride of Portable Hole Full of Beer: The Book of Neurotic Fantasy. Unfortunately, it's no longer free (it's now $1.99).