I had done one run as NG (I assume that's when you start a new game and don't load it from a previously finished run) and my time was recorded. Then, I did a NG+ and the Livesplit stopped right before the credits--It was the part right when I grabbed the revolver for the dual vs Ocelet on the plane.

Edit. I'm playing the PC version of the game.

Edit 2. After having a little bit of time to sleep on this and review the rules that are on this site, my educated guess is that I probably used some camo before the fight vs The Boss which is not allowed and that is what stopped the clock.

You might be missing a split, or the game split earlier because you re entered a room, which caused it to split incorrectly.