In the GM game, black was right to play on when only a piece down. The position was rather locked up and he still had drawing chances. I honestly wouldn't have been offended if my opponent had played on in the rook-down scenario either. He's got the connected passed pawns, and while it's pretty obvious white can stop them easily, I'd give him the benefit of the doubt and assume maybe he doesn't see it. However, once those pawns get stopped it's just rude to keep playing since no GM in the world is going to botch that ending. Hell, even a C class player can finish that off correctly.
Ironically (given some of the earlier comments) the only excuse would have been if this was live instead of cc. If white was under extreme time pressure I could see playing on (although I'd offer a draw first), simply because it's possible he flags prior to the mate.
The game involving the GM (post #11) was played at three days per move. Makes me wonder what exactly was going on. 
(I'll let you figure it out, if you haven't done so already)
In the GM game, black was right to play on when only a piece down. The position was rather locked up and he still had drawing chances. I honestly wouldn't have been offended if my opponent had played on in the rook-down scenario either. He's got the connected passed pawns, and while it's pretty obvious white can stop them easily, I'd give him the benefit of the doubt and assume maybe he doesn't see it. However, once those pawns get stopped it's just rude to keep playing since no GM in the world is going to botch that ending. Hell, even a C class player can finish that off correctly.
Ironically (given some of the earlier comments) the only excuse would have been if this was live instead of cc. If white was under extreme time pressure I could see playing on (although I'd offer a draw first), simply because it's possible he flags prior to the mate.