Getting back on topic here, I agree with Dolphin when he said that
"It is unreasonable for anyone to insist on voting to end just because he lost in the first few turns."
When they start to waste your time by delaying the game, you have two choices. One is as Piggy said, just agree to vote to end and know that you are the true winner of the game. The problem with this is that it creates a precedent, your opponent will know this kind of thing works and will be more likely to do it again in the future. Even if you don't care if it happens to you, others (as evidenced by Billy) will.
The second option is to just keep playing out the game until they figure out it's not going to work. It will take more of your time, but you can take satisfaction in crushing your opponent's remaining troops. I'd also recommend to not respond in the chat as soon as your opponent starts asking for a vote to end, as it will be more obvious to them that you're not willing to settle for anything less than a win, so they'll be more likely to surrender. Finally, if the boot times are long there's nothing stopping you from opening up a new tab and doing whatever you want elsewhere on the Internet. You're also free to join another Warlight game, just keep in mind that you'll have to spend a couple minutes each turn on your remaining one.
I'm partial to the second option, simply because it discourages the stalling of games, which I feel is something no one in the Warlight community wants. In the end though it's up to you to decide what option is more preferable.