I want to prepare a homemade bread, wrap, pita, or tortilla-like food, something to make in advance on weekends, to later fill with typical sandwich fillings, such mayonnaise, cheese, sliced meat, and vegetables on the day that I want to eat it. A loaf of bread seems to last only a day, then it is too dry to eat and if stored in the freezer, it loses flavor. Is there any special kind of break, wrap, pita, or tortilla-like food that lasts for almost a whole week?
Firstly - shop-bought "packet" bread will keep for several days because it contains a lot of preservatives.
In his excellent book Bread Matters, Andrew Whitley claims that home-made sourdough breads with very long rises have better keeping properties than home-made bread made with baker's yeast and short rises. This, he claims, is because the sourdough yeast cultivates a culture of friendly bacteria and an acid environment, all of which become natural preservatives. My experience seems to confirm this.
Bread recipes containing egg, oil or milk tend to keep for longer than those without.
As @SAJ14SAJ says, bread freezes very well. Loss of flavour in the freezer is not a commonly recognised phenomenon.
One option is to slice a loaf of bread, bag it and freeze it. Take as many slices as you need at a time. It will defrost very quickly at room temperature, due to its low mass and high surface area.
Another option is to make rolls, part-bake, and freeze. When you need them, take as many rolls as you need from the freezer, and place in the oven, to both defrost and complete the baking. You will get fresh baking smells and flavours from this.
I suspect that home-made unleavened breads (pita, chapati, tortilla), without added preservatives, will not last long out of the freezer. Their advantage is that with no rise, they are so quick to make that they can be made fresh on-demand.
I admit, this doesn't exactly answer your question, but to expand on slim's suggestion for flatbreads -- if you're willing to give up fridge space for this, and have a little bit of time & fuel each day for cooking, I'd recommend the recipes in the various Artisan Bread in 5 Minutes a Day series of books.
You make up the dough, let it proof, then refridgerate it for up to two weeks. During that time, you can pull it from the fridge, throw a little flour on top, grab a ball of dough out, and bake. Or, in my case, I preheat a skillet, stretch the dough out into a disk, and cook it as a flat bread. It only takes a minute or two per side if you keep it thin & the pan's hot.
You can refrigerate it after it's baked, but you might want to warm it back up if you're going for a wrap-type sandwich, so it's flexible enough.