Layered themes issues (child theme of a child theme)

I have a strange issue occurring. I’m currently working a Multisite install where essentially I have 2 sites and one looks almost identical to the other but has subtle differences. Every site I work on, I create a child theme which sub classes this master theme that I use as a framework of sorts. For this setup, it seemed appropriate to make yet another child theme to cover the subtle differences of the second site. So essentially, here’s my theme hierarchy:

Master Theme <– Main Site <– Secondary Site

The issue I’m having is, template files from the secondary site are not falling back to the Master Theme. For example, if you leave out archive.php in a child theme but include it in the parent, WordPress will fall back to the parent and use it’s archive (instead of WordPress’s default archive fallback). I want the same functionality to occur here, except I need the secondary site to fall back 2 levels instead of one.

Does WordPress not do this by default or did I just likely make a mistake in my setup?