Most go literature is not too clear about when to end a ko fight. You read that if the ko threat is bigger than the ko, you should answer the ko threat and continue the ko fight. This implies that if the ko threat is smaller than the ko, you should ignore the ko threat and end the ko fight. This is wrong, this will cost you several points.
See the problem below, figure out the sequence that wins for Black. There are no captured stones, there is no komi (komi = 0).
The only winning sequence is shown below,
followed by the closing moves.
So, the first ko threat already is smaller than the ko, but if Black would have ignored it, he would have lost by 1 point.
There happens to be a rule that easiest makes sense when, quite naturally, the ko threats are played in decreasing order. One should end the ko fight if the sum of the values of the current opponent's ko threat and the next own ko threat is smaller than the sum of the values of the ko and sente after the ko.
The value of the ko is 15 points, the value of sente after the ko is 3 points, together 18 points. The value of the ko threat Black ignored is 9 points, the value of the next ko threat is 8 points, together 17 points. So Black ignored White's ko threat for good reason according to the rule, here it happened to be the only way in which he could win.
In a normal game it is difficult to calculate some of the values, but prolonging the ko fight a bit longer usually is a good idea. You see this when replaying pro games, the pro's may not know about the rule but they apparently have an excellent feel for the score.