What's the definition of falling due and how did its sense materialise? Please compare it against "due"? I'm mindful that it's an accounting/business term: here are its matches on Google Books.
I'm not after the etymology of each word, but rather how falling + due (ostensibly) denotes maturity?
http://dictionary.cambridge.org/dictionary/business-english/amount-falling-due-after-one-year?q=%22falling+due%22 seems to connote that falling due = due?