How To Lose A Won Rook-and-Pawn Ending

GUERNSEY turned into something of a nightmare tournament.
I had winning positions in six games and was much better in the other one, but I ended up losing five of them before converting the last two into wins.
That gave me a score of +2=0-5 for a Fide rating change of -24.4 (not as bad as it might have been - all five losses were against higher-rated opponents).
Of course I am blaming the heavy cold I was suffering from, but my round five loss had more to do with lousy endgame technique.
Here is the position after White's 25th move.

Black to play in Ruediger von Saldern (1894) - Spanton (1858)

Black is clearly much better - the only question should be whether White can somehow hold on for a draw.
25...Kf8 26.Rb3 Rd7 27.Re4 Re8 28.Reb4!?
An interesting choice. There is a rule-of-thumb in rook endings that, for the side with the advantage, two rooks are better than one, and none is better than one. In other words, the defending side's best chance of a draw usually lies in getting an ending with one rook aside. However, here RvS opts instead for pressure against my b-pawn.
28...Ree7 29.Rb6 Ke8 30.Kh2 Kd8 31.f3 Kc8 32.h4
Stockfish8 and Komodo9 now agree Black is winning rather than just much better.
32...h5 33.Kh3 Rd1 34.Kg3 Ra1 35.a3 Rae1 36.Kf4 R1e2 37.g3 R2e6 38.g4 Rf6+ 39.Kg3 hxg4?!
The analysis engines are happy enough with this although it does give White the prospect of creating a passed pawn on the h-file. I rejected 39...g6 because I thought 40.g5 might be good for White. (The engines prefer 40.gxh5 gxh5 41.R6b4, rating Black's advantage at around 7/10ths of a pawn).
40.fxg4 Rfe6 41.h5 c5??
MUCH disliked by the engines. Two question marks might seem excessive but White is now better, according to the engines. The point is that after an exchange of one pair of rooks, White's king is much better able to support his advanced kingside pawns.
42.Rxe6 Rxe6 
Better is 42...fxe6!, which gives Black two isolanis, but more importantly gives counterplay thanks to the passed e-pawn.
43.g5 Kc7??
Black is now lost!  43...Re8 was vital to try to restrain White's coming passer.
44.Kf4?
Better was 44.Rf3, eg 44...Re7 45.h6.
44...b5?
Again necessary was 44...Re8.
45.Rh3
If 45.Re3? then 45...Kd7, and if 46.Rxe6?? then 46...Kxe6, eg 47.h6 gxh6 48.gxh6 Kf6 49.h7 Kg7 50.Ke5 c4 51.Kd4 Kxh7.
45...a5 46.h6 gxh6 47.gxh6 Re8 48.h7 Rh8 49.Kf5 c4 50.Kf6 b4 51.axb4 axb4 52.Kxf7 Kd6 53.Kg7 Rxh7+ 54.Kxh7 Kd5 55.Kg6 Kd4 56.b3??
56.Kf5 wins, eg 56...c3 57.Rh4+ Kd3 58.Rxb4 c2 59.Rb3+ Kd2 60.Rc3.
56...c3??
Played instantly, whereas 56...cxb3 is a trivial draw.
57.Rh4+ Kc5 58.Rc4+ Kb5 59.Kf5 1-0