Do the stories reset every day?

Stories never reset. Once you have made progress in a story, it will stay, so that you can pick up where you left off the next time the faction of that story pops up.
Keep in mind that the bard tells a story of a different faction each day. You can view his schedule, as well as the remaining time of the current story in the Tavern:

After having completed a story, you can battle/farm (depending on the scope of your success) every stage as many times as you want.