Apparently, James Kirk's fighting skills increased after his shirt ripped, or maybe it was a coincidence that he never seemed to lose when this occurred. Am I just remembering incorrectly, or did Kirk really have an undefeated record when his shirt ripped?
Captain Kirk got his butt kicked by Leela in Where No Fan Has Gone Before, despite his shirt being ripped. Also, Spock messed him up in both Amok Time and The Paradise Syndrome. It would be difficult to believe that having half a bridge fall on him in Star Trek: Generations didn't rip his shirt, but it isn't visibly torn.
If you include books, Omnidon beats Kirk to a pulp on multiple occasions in The Flight of the Phoenix and The Fate of the Phoenix. I'm sure there are many other examples outside of television and films, but I don't recall any others.
As per my comment, no, Kirk did not always win fights when his shirt ripped. "Amok Time" is one counter-example.