Welcome to the forum
In my time I've done an awful lot of doc -> html (filtered) -> epub conversions, but I have to admit that I've never had this problem.
Is it possible that some of your chapter headings are styled as 'Small Caps' in the .doc file? That may explain why they look like capitals in the .doc but they're not converting to epub or mobi because SmallCaps are not supported.
chapter two and ChAPTER SIX would look like CHAPTER TWO and CHAPTER SIX in MSWord if styled as SmallCaps even though they contain lowercase characters.