At last, Black has sufficient material on hand to fend off the attack. Two of White's pieces and the h-pawn are now really en prise and an exchange is the only way to prevent serious material loss.
31. Be4d5 Bc4xd5
31. ... g6xh5 would win a pawn, but leave Black's king exposed.
White has extricated the pieces which were all en prise, but the endgame favours Black, for the following reason: Black has the outside passer. This means that, if the pieces were removed and only kings and pawns remained, the White king would have to travel to the a-file to stop Black's passer, whereas the Black king would need only travel as far as the c-file to stop White's passer. In the ensuing race to get back to the k-side, Black's king would be closer and White would be the loser. Therefore, it is imperative for White to harry the a-pawn and either trade it off, or force it onto the b-file where it will no longer be a passer. White is fighting for a draw now.
35... Bg7d4 36. Nd5f4 Qf8f6
The White knight had threatened to go to e6 or g6; the text move stops both.
37. Kg2f1
White now threatens 38. Nxg6+, QxNg6; 39. Qd8+, K any; 40. QxBd4, winning a pawn.
37... Bd4b6
Black parries the threat, but now allows White to achieve his purpose in rendering the a-pawn less dangerous.
38. Qc7b8 Kh8h7 39. Nf4d5
It is now unavoidable that the a-pawn migrates to the b-file. White's drawing chances are improving slightly.
39... Qf6d4 40. Nd5xb6 axb6 41. Qb8c7 Kh7h6
We have now arrived at what Reuben Fine, in Basic Chess Endings, claims is the most difficult and complicated of all endgames: kings, queens, and multiple pawns.Very few general principles apply to these endgames beyond: a) each king should stay close to his pawn(s), and b) perpetual check is the likely outcome.
42. Qc7c6
Both sides must tread carefully and avoid losing a pawn to a surprise forking-checking manoeuvre. With Qc6, White pins the g6 pawn, preventing its advance; and keeps the b6 pawn under constant watch; and defends the White c2 and f3 pawns.
42... Kh6g5 43. Kf1g2 b5
?? Ouch. This is the sort of mistake which can occur only in correspondence chess: one has several games running concurrently, one writes down a list of probable continuations/variations, but at the critical moment the eye slips down one row and one makes a move out of order. Of course, Black intended 43. ... Qc5; 44. Q moves away, and THEN 44. ... b5.