You see that you are many points behind your opponent, and the opportunities to catch up are limited. What can you do?

• Hope your opponent will screw up. Try some really complicated invasion, or attack. This might work. However it shows a lack of respect for your opponent. This is Go, after all, not Chess. Your opponent got ahead of you - give him the credit for that.
• Continue playing - maybe your opponent will lose her link and disappear. It happens.
• Continue and lose by a large margin. This is usually quite depressing, and you will probably not learn anything more from the game. Remember, this is not a Greek tragedy. There is nothing to be gained by going down in flames.
• Run away. That is very common. Also considered very rude.
• Resign, leave the table and try to forget it ever happened.

1. Try to figure out why you are losing - which move was bad for you? You may not be able to do so, but try.
2. Resign. Cheerfully.
3. Thank your opponent for the game. Perhaps even congratulate her.
4. Start a new game with the same opponent. Perhaps try to repeat the same game without the bad move(s).