In Peruvian Jungle, shooting the jaguars has little, if any effect. Lara can just dodge and heal as needed. Apparently it is a canned sequence where the two jaguars cycle through the area, and after some number of cycles, the sequence just ends, even if Lara never shoots either of them.

 

I always just shot them between the eyes with fire arrows, but didn't know the battle auto ends after a specific amount of time.

This came to my mind earlier on.  I've been ploughing through my NG+ and just got to the helicopter boss.  At the end, after I'd used nearly all my medicine due to pressing the wrong buttons on the controller because I've been playing Hitman Sniper Assassin mostly in the last week, it was a bit odd.  I had Lara crouched behind the round thing behind which she can crouch when the helicopter minigun is firing, healed, there was one guy (maybe two?) left to shoot.  Thing is, while she was crouching behind that thing the 'copter just blew up by itself.  Is that on a timer, too?  I haven't tested the jaguar fight.  I could try a test on the helicopter boss on my other Xbox, that's not been synced.

Interesting! I'll definitely experiment more next time I replay. I got sidetracked by Extra Life and need to buckle down and finish this walkthrough. Then I'll go back and check. I'd be interesting to hear what you all discover about this.