Patience I / II : Increases HQ chance, while reducing success of catching a fish by 40% (Inefficient Hooking).

You can use that, and just normally keep fishing. Just means Fish are 40% more likely to get away (while having higher HQ chance).

Now 'Powerful Hookset' and 'Precision Hookset' negate the 'Inefficient Hooking' for the one pull they are used on, -if- it's the right skill for the Fish.

Usually Powerful is for big/heavy fish and thus strong tugs, while Precision is for smaller fish and thus light tugs.

The Fish can still be caught even if you use the wrong hookset - just has 40% extra chance to get away.
(Some people also say that inefficient hooking doesn't matter if your gathering stat is far above the fish, but I'm not sure about this.)