strange ending

Both Deep Fritz 12 and Deep Rybka 4 evaluate this as won for White even afrter 35-move deep analysis, although I can draw easily by keeping my King where it is and using the rook to check when required. I drew this game against a player rated 200 above me.

Sorry about the error -here is the correct inverted board.

In your diagram, it looks like White queens easily after Kf5.

Oh, I see! Rh1 lets you continuously check the King.

You should fix the diagram in the OP, it is reversed. In that diagram, white has a win in 34 starting with 1. Kc4, but actually any king move wins. However, in the correct (flipped) position, black can indeed defend.

Note that any engine without a good tablebase will not be able to fully evaluate such a position. The engine knows that white clearly has the advantage but cannot know for sure if she can convert it. Engines don't understand the kind of logic you use to evaluate this position, they just calculate lots of lines.

However, you can equip your engine with a six-man tablebase (if you have tons of hard drive space), in which case the engine will know this is a draw.

white was supposed to win