I assume you are selecting the style in LayOut? It sounds like the style you are selecting is set to show section cuts. You cannot edit the style's properties from LayOut so instead, set the style for the scene in your Sketchup model as desired and edit it if needed to not show the section cuts.

If you share the LO file I will show you how to make the setup if you aren't sure how.

Are you still using SketchUp 2017 as indicated in your profile?

FWIW, since the release of SU/LO2020, I've created a collection of customized styles that are typical of the ones I use in documents I create in LayOut. Some of these styles have section cuts turned on, some don't. These can then be selected in LayOut instead of being set for scenes and I only need my working style in the SketchUp model which helps a bit in controlling file size. In versions before 2020, the styles were set in SketchUp because changing the style in LO resulted in a modified scene and many of the scene properties would no longer carry over if changes were made to it.

@unknownuser said:

When I go to styles and select Construction Documents... Any ideas?

First thing: Don't change the style in LayOut. Set the desired style for the scene in SketchUp. Avoid doing anything that results in the scene showing as modified in the SketchUp Model panel.

As for why half your model is disappearing, it's hard to say without seeing it. Upload the LayOut file so we can take a look and give you an answer.