Since my opponent's passed pawn was further advanced than mine, I had no choice but to keep checking his King. As he had already declined a draw, it would have been discourteous to offer it again. This is one of the consequences of playing an opponent with a rating much higher than your own --- he has too much to lose by agreeing to a draw.
The idea of getting into another Queen ending like this one is now so repugnant to me that I'm reluctant to join any more games. Can you blame me? Show this game to a beginner, and you'll turn him off chess for life.
52 ( +1 | -1 ) On the other hand...If I played the game that you played, I would never stop bragging about it. I would love to be able to say that I forced a draw against an opponent whose rating was 241 points higher than my own, a draw that he had earlier refused to accept, and that the outcome was only possible because I had played the last 35 moves of the endgame impeccably. Quit chess?! I'd be challenging that opponent to a rematch! * "Omnia ad opinionem suspensa sunt." -- Seneca ('Everything depends on the view you take of it'.)
52 ( +1 | -1 ) Trading queensImagine the position after 58...Qxb5. White would have queened first, but what then? If White activated his king, your pawn would then have been able to reach its promotion square. If White didn't activate his king, his queen by herself could neither have checkmated you nor forced your king to abandon your pawn. In short, if you had traded queens, the unwinnable nature of the game would have soon become self-evident.
31 ( +1 | -1 ) My analysis (which might have been wrong) indicated that the White Queen could have forced my King away from the pawn --- which is why I rejected the exchange of Queens at move 58. Of course, if I was wrong, then my technique is inadequate, which only adds to my exasperation.
25 ( +1 | -1 ) For future referenceOne ought to know, in general, that a Q vs. RP or BP on the 7th rank (and only a RP or BP on the 7th rank) is drawn due to the stalemate possibility, unless the king can advance to threaten mate. So, for example:
58... Qxb5+ 59. Kxb5 h5 60. a6 h4 61. a7 h3 62. a8=Q h2 with a book draw (once the Queen comes to g3, ...Kh1 is stalemate).
21 ( +1 | -1 ) Take heart!Chessmaster 9000 repeatedly plays the position to a draw, but give yourself a break! After all, "Endgames with the queen and pawns on both sides are among the most difficult in chess" (Keres).