In Storyline, how can I prevent the Player Next button from working until all layers are visited?

If you were to upload a .story file here with just that slide in it (and the content obfuscated), someone could tell you what the issue is, probably within hours.

After you double-check that the player settings for the slide are not going to override this slide (as others have suggested), put something on the last layer to force the "Next" button to appear.

A simple way that I have done this is to look at the timeline for the layer, then add a  cue point near the end (maybe 3-4 seconds before the end). Then add a trigger: Change state of Next button to Active when timeline reaches Cue Point #1.

The "next" button should then become enabled when the timeline reaches that point. You can also set the trigger to just force the state change at the end of the timeline and ignore the suggestion about a cue point.

Also - check the placement of the trigger in the trigger panel (I would show a screenshot but I am not able to capture one at the moment). Triggers are executed in the order they are listed, so if the "change state of Next button" trigger is way down the list, then it's not going to happen until all the other triggers have been tripped. So move that trigger to the top of the list (or as near as you can) and then see whether that solves the problem.

And as CarlFink1 suggested - share a copy of the slide and you're likely to get a rapid response.