The way it is designed now each artboard exported to the same page are in an artboard HTML element. Each artboard is one big container containing all of the visual objects.
When you switch to view another artboard the current artboard is hidden and the new one is revealed. There’s not really a way to have one element contained IN an artboard visible all the time.
But there are some things you can do to get what you want.
You could create a separate artboard that is always visible if you know if some code. You would set it’s display to block or flex and then have to remove the artboard from the CSS artboards array (so it isn’t hidden when you change artboards) and probably set it’s z-index to 1 or more so it’s always visible above other elements.
Otherwise, I would suggest you create a component and have an instance of that on all artboards.
For example, if you have a navigation bar you want always visible create the layer group, convert it to a component and then create instances (duplicate it) and place it on each artboard.
If you need to change it, since it’s a component, the instances will be updated with any changes. Does that make sense? Let me know if this helps and maybe an example and I can help you with any code or setup.