First a disclaimer: yes I know that the Hundred Years War was not one war that lasted for a hundred years. I know that it was actually a series of individual wars between the English and French nobility over English possessions in France.
My question is why did conflict over English held land in medieval France drag out for as long as it did? What were the factors that prevented a quick and rapid resolution to the conflicts?
As I'm sure you can imagine, it's complicated, but here's a rough sketch.
The main reason, in my eyes at least, is that the English had a lots of success in the 14th century (the first half or so of the 'Hundred Years') but failed to capitalise on it effectively. They won several huge battles (Crecy, Poitiers) and had the French economy on its knees from pillaging and sowing dissent. They even captured the French king. They held all the cards, but because they wouldn't compromise on various things they failed to make satisfactory progress in the peace treaties that followed these successes. That meant that the tensions that existed before the treaties continued to exist, and so armies kept being raised and so on and so forth.
There's also the fact that, in this medieval context, there couldn't really be a winner or loser in the modern sense. It was incredibly difficult to marshal the army necessary to crush the enemy thoroughly enough to impose terms of annexation or claim their throne, especially a country as big as France. You couldn't really occupy more than a few major settlements. And the English had to ship their army across the channel and live off what they could pillage, and the tax money required to set that in motion had to be passed through Parliament. So all these things mean that there was very little decisive action, leading to more of a bubbling skirmish punctuated by periods of ceasefire.
But it's a complex and long period of history that I'm sure someone else will have a more detailed understanding of than I do, I haven't studied it for a while.