Interesting! Yes I think to some extent we've all had similar experiences but probably under very different circumstances (school chess, club chess, tourneys, between friends etc).
Chess is a very dynamic game, in the sense that beating someone doesn't always mean you're necessarily better or understand the game better, it may very well be so. Of course this is because of the inherent nature of the game where making mistakes is so common and part of each game. Point being you may be 100 times better than someone but if you're the one making the last crucial mistake of the game you will lose.
As mentioned in some of the other replies, approaching the problem from a complete psychological angle is possible, but I have another suggestion for you, which is technical and stays chess-related.
If you say you've played so many times vs this person A, since the time you started learning the game, then you must surely be able to tell "how most of the time you end up losing to him". This is important because if say, you always out play him in the opening but end up failing at converting your advantage in the middle game due to silly cheapo tactics from your opponent, then you can tell yourself "ok in the middle-game I should double check the tactics vs this guy...".
Or alternatively, if most of the time you end up messing your openings, then you can forget known opening lines and just play solid-development style against him.
Finally if you know it's the endgames that cost you the games, then either try to finish him off before an endgame, or if you do reach one, again go for simple plans that work well (assuming you've reached the endgame with some advantage), i.e. cutting the king, simplifying the position with key exchanges, covering space with pawns,... the usual stuff.
Finally if you're saying that each time you lose to him in a completely different way that you've ever lost before, then again, same idea can be applied, you should always assume your opponent is the best player and will find your mistakes, this means you should never assume "ok I'll play this hoping he won't see the check or the fork...". In chess you don't hope, you plan things out and follow your strategy.
Long story short, I think you can overcome this rather strange nemesis of yours, by simply paying attention to "the ways" you lose to him/her. Get yourself some stats on the losses, and start working things out.