When you set your defensive depth to 71 or higher, with 71 being the switching point, your team AI starts to press and track runs on defense, as opposed to just passively letting the other team progress through you. The significant thing about this is there is no appreciable loss of stamina at least for the first half.
Again, this does not affect your stamina. Your players will lose the same stamina at 50 depth as at 71 depth. This is key.
If you use Press after Possession Loss, you will see your team start to get knackered after 45 minutes. At 71 depth, it's a constant press and cutting of angles, for no cost.
You'll start to feel the effects of stamina loss around 70-75 minutes, but so does the other team. And you can sub 5 players, so thats could be your entire back line and a CDM, or two CBs and two CDMS, etc.
I've been trying to figure out how teams have such better AI than me, and this is what it is. It's been working for me for the most part. Some players are good enough to get around the press, but it requires having people who can cross the width of the field to do so, and not every player can. For everyone else, it feels like I'm cheating.
Have at it!
EDIT: Adding that you can keep your defense on "Balanced" and this works. You don't need, and shouldn't use, one of the "Press After..." tactics. Forget those. Balanced Defense, 71 depth.