I'm going to break this idea up into the easy part and the hard part. The easy part I call easy because I have answers; the hard part is where I'm stumped.
Last Shabbos I discussed with my son the following question quoted by R' Scheinberg in his Mishmeres Chaim (a sefer which, along with the Mefa'aneyach Tzefunos, is a staple of oneg Shabbos): A basic principle in halacha is the idea of chazakah -- the assumption that a status quo is maintained until proven otherwise. For example, a kohen who sees a nega on the walls of a house may close the door and declare the house tamei without having to worry that the size or shape of the nega changed between the time of his observation and the time of his declaration. If so, why do we treat bein hashemashos as a period of safeik yom safeik layla -- why not say that since it had been day until the moment of twilight, the chazakah of it being day continues until proven otherwise at which point it become definitely night? Why is there a twilight period of halachic doubt if it is day/night when we can resolve that doubt using the rule of chazakah?
I have at least three good answers to this question -- one suggested by my wife, one by my son, and one by myself, roughly corresponding to a sevara, to a Rogatchover-ish idea, and a Brisker-type solution. I don't want to make it too easy, so I'm going to give away the sevara solution and you can work on the others. Tosfos (Gitin 2b) writes that chazakah cannot be applied to a situation which by definition is subject to change, e.g. a nidah is not considered to have a chezkas issur because we know at some point that she will stop seeing blood. Here too, we know that it will not remain day forever and the sun will eventually set; therefore, the status of day cannot be defined as something which is called a chazakah.
Feel free to comment away if you can think of a Rogatchover-ish or Brisker answer or even better, a pilpul answer, and then fasten your seat belts for part II.