A more reliable check is to compare an address of a thing on the stack at api boundary with the current address of things on the stack. SpiderMonkey, the JS engine in Firefox, used something like that in past to stop run-away recursion or at least to switch to slower algorithms with bounded stack usage.
PS: It's not one single function, not direct but indirect recursion.
This makes me wonder: does any of the popular xml libs have a sort of safe mode, where custom entities and similar features are disabled, those schema urls ignored, and namespaces just flattened (and whatever else I forgot or don't even know about)? You know for when I know I only need to parse simple xml files that should contain a couple plain tags and attributes, and want to reduce attack surface.