At what point does the conflict reach its climax?

Simple answer...when it needs to.

The normal storyline arc used in most novels has the climax occurring fairly close to the resolution of the book, with a long enough wind-down to avoid the feeling of an artificially truncated ending but not so much that the climax has time to fully wear off.

But that's not a universal thing. Stand by.

In short stories, there may be no resolution. You may literally end on a question or climax. Open-ended short stories carry a punch. Other short stories may hit you with the climax, resolve quickly, and get out of Dodge before the shock settles.

In longer works (novellas or novels), you may actually start on a climax point and then work your way into HOW you ended up there. Many Excellent works are written out of order...either starting in the middle of the climax and working back through the hows and whys or skipping forward and backward in time.

Which leads me to... You CAN have more than one climax point. Is it the usual way? No. It confuses the heck out of some literary purists, but it is possible and powerful. The longer the work, the more likely there will be more than one climactic scene. They may vary in intensity, of course. While many people imagine the storyline arc as a skewed bell curve, it can actually be a series of mountain peaks, when graphed.