It seems that you're missing the point.
No one is challenging your right to play the game until the end, however, you are not allowed to stall a game using vacation days(so called "vacation abuse").
http://support.chess.com/index.php?_m=knowledgebase&_a=viewarticle&kbarticleid=691&nav=0,6
And I dont think that chess.com would declare "completely and hopelessly lost" a game in which only a GM would find a forced win. It had to be a game where even a moderate player could win the ending against GM.
Maybe chess.com could show an examples of such games so everyone would have a better info.
When I turn on vacation pauses, this website pops up a warning that I'd better not be trying to use the pause to prolong "hopelessly lost games."
The first time I read the message, I chewed my lip and worried the site would punish me because I was behind in at least one of my games, but I wasn't sure if being behind was the same as "hopelessly lost."
The next time I read the message, I was behind in most of my games. At that point if Chess.com was going to punish me I didn't care. Losing was worse than anything they could do to me. I figured if they kicked me off the site, I'd just go somewhere else.
Since then I've thought a lot about what a "hopelessly lost game" is. I thought back to the Anand-Topolov games that ended in draws and the games both champions lost, after making 60 or more moves.
I've concluded a couple of things about Chess.com's threat:
1) No one has the godlike ability to identify a hopelessly lost game.
2) Amateur and professional chess (Anand-Topolov) are very different. In a professional game, observers can expect both players to make good moves and few blunders. A professional game can eventually become a hopelessly lost game, and the loser will resign rather than make a fool of himself. But in an amateur game--even one in which the opponents have very different ratings--no one can say that the higher-rated player will never make a mistake.
3) Very few amateur players (whom I've encountered) know how to win an endgame quickly. You all try to win with a knock-out mate, and when you're playing a less experienced player you usually win that way. But when your opponent manages to reach the endgame, you can't figure out how to knock her out in a couple of moves.
In other words, I don't believe there is such a thing as a hopelessly lost game. And even if you show me one, I defy you to be able to explain to me why the loser in an amateur game doesn't have the right to finish the game and learn from the experience.