The script never hits a 404 so it continues to load.
If I am looking at this correctly it won’t ever hit a 404, and it shouldn’t ever hit a 404.
You are loading a page template, the finding and loading of which is going to be done by the main query. That page is always going to be found– ie, not 404.
Your secondary query– the one that is loading the posts– is inside the page template. It doesn’t matter if there are posts or not, it won’t trigger a 404. That part is long past by the time the secondary query runs.
I think this is fundamentally just a design problem.
I don’t know how your AJAX works, but what you should be doing is checking for the presence of posts returned by the query, not for a 404 returned by the page. You stop when you get 0 posts. And you should really be using the AJAX API for this as well.