They have to be set to "ongoing" otherwise once they have been run once they will no longer show up (or at least not for another day/week depending on the frequency setting).

All of the policies in question are all set to ongoing. These policies were working not so long ago and the issue was noticed prior to updating to Casper Suite 9.6

Any network limitations applied to the policy that you may be overlooking? Like only showing up under certain Network Segments, or only when on a wired connection, etc? Or any client side time limitations that would make it only show up at certain times of the day?
I would look carefully through all the settings in the problem policy and compare it to the one you create from scratch that works. There must be something different between the two of them.

Something else you can try on a lark; disable the policy, save it, then enable it again and save. I'm wondering if somehow even though its showing its enabled, it actually isn't and is some kind of visual glitch. My guess is probably not, but if combing through it carefully to make sure nothing is amiss doesn't reveal the problem, you can try the above just to see what happens.

Do you have multiple applications and scripts in this policy?