Button on base layer needs to stay disabled

Jose is right: The layers have triggers that change the button states: first to Disabled and then back to Normal. That's why they don't stay in the Visited state. 

I suggest you delete all those triggers. Instead, to prevent the user from clicking the buttons when they're on a layer, do this: 

• Open Slide Layer Properties by selecting the layer(s), and then clicking the gear icon in the lower right. 
• Select "Prevent the user from clicking on the other layers." That will prevent them from clicking the buttons on the base layer.

Note: If you want to make the buttons look disabled, you could cover them with semi-transparent shapes. In fact, that would also prevent the user from clicking them.

Or here's another option: On each layer's timeline, expand the "Base Layer Objects" to show the list of everything on the base. Deselect the eye icons for the other buttons.

By the way, you know how when you answer a Multiple Choice question, only 1 button can be selected at a time? That's a button set. Here's more info: Storyline 360: Working with Button Sets | Articulate - Community