Is there any Biblical Basis for 400 years of silence between Old and New Testament?

When I was researching about the deuterocanon (or the apocrypha, as most Protestants call them) I stumbled upon the notion that God was silent during a period of 400 years between the end of the Old Testament (after the Prophet Malachi) and the beginning of New Testament time (namely the appereance of John the baptist). From a Protestant point of view where the deuterocanonical/apocryphal books are not considered scripture, there is indeed a 400 year gap in revelation -- no prophets, no inspired writings, nothing. From a Catholic, Orthodox and Assyrian Churches, point of view however there is scripture written and inspiration taking place during that period and there is no gap (at least not that long) in Gods revelation. Now, when looking for reasons why christians consider the deuterocanon/apocrypha inspired or not I am sometimes told that those writings originated in a period where God was silent and thus cannot be considered scripture (like here , here or here ). To me this is: 1. A circular argument (apocrypha are not scriptural -> God was silent 400 years -> in those 400 years no inspired scripture was written -> apocrypha are not scriptural) or 2. There must be another reason to believe God was silent for that period. This reason would break the circle in (1) and make the stated argument valid. **My Question: What biblical basis give adherents of a large time of Gods silence between the Prophet Malachi and John the Baptist beside the (perceived) fact of missing inspired scripture in that period?** A best answer could simply cite the prophet X in saying: "Listen, God will be silent for 400 years before the fulfillment of time." and then stating that this fulfillment of time has come with Christ. But there may be more to say to that matter ...