patience is key. turtle always beats the hare.
Stalling in Online Chess

Your opponent is allowed to take his full time to think about his move. Perhaps he likes to move in all his games and come back to your game.
Is it annoying? Yes. Is it rude sometimes when people do this? If they're just trying to put off losing, maybe. Should it be against the rules? I don't see how it could be, that would be shortening the time control, which is already an option.
It has happened to me in the past where a player takes all their time on every move. The game sure went slow, but eventually it ended. It was pretty annoying that it kept happening after my opponent was clearly lost. So on one hand I'm usually sympathetic to this kind of stuff. On the other hand, you did sign up for a tournament called "The Logest Tournament Ever" with a 14 days per move time limit, you're kind of asking for it.
In a game with a member (not naming him/her for privacy reasons) I'm having in The Longest Tournament Ever my opponent keeps stalling. I have set up conditional moves but he/she seems to be trying to prolong the game. Every time he logs on he only makes one move which is met by my conditional move but he just doesn't move in this particular game for a long time while moving in his other game against me. I think this should not be allowed.