Kimchi goes pleasantly sour in about a week and unbearably sour by week three, even in the fridge: is that just what happens?

Switched from one two litre jar to three smaller ones and it solved most of this without changing the recipe.

A big jar is opened repeatedly over three weeks, and every opening introduces oxygen and warms it. Three small jars means two of them sit unopened and cold until you get to them, so week three tastes like week one did.

Some of it is the nature of the thing, but four weeks is achievable and three variables decide it. In order of how much they matter:

Temperature, by a distance. Fermentation does not stop in a fridge, it slows down, and the rate changes steeply with a couple of degrees. A fridge that runs at 6 or 7 will take your kimchi through the same range in roughly half the time of one at 2 or 3. Most domestic fridges are warmer than people think and the door and top shelf are much warmer than the back of the bottom one. Put a cheap thermometer in the spot where the jar actually lives before changing anything else, this is usually the whole answer.

How far you take it before it goes in. Two days on a warm counter is a lot. You are handing the fridge a jar that is already well populated and well into its acid production, and the fridge only ever slows what is happening. Going in earlier, when it is barely tangy, buys you real time at the other end, because the whole curve shifts.

Sugar in the paste. The sugar is food, and it is the fastest food available. A paste with a generous amount of sugar or fruit gives the early sprint more fuel. Cutting it back slows the first two weeks noticeably.

Salt at 2 percent is reasonable and I would change it last, not first.

Adding the mechanical things, which are less glamorous than the biology and easier to fix.

Keep it submerged and keep the headspace small. Once the jar is half empty there is a lot of air over the top, and the surface behaves differently from the body of the jar. Moving the remainder into a smaller container when you are through half of it does more than it sounds like it should, and it is also when most people notice things going strange on top.

Press it down every time you take some. A clean utensil, and push the rest back under the brine. Two seconds.

Do not keep dipping the same fork in. Every trip introduces something, and by week three the population in the jar is not the one you started with.

On the practical answer to your actual question: make the same amount but in two smaller jars. Open one, leave the other sealed at the back of the bottom shelf. The unopened jar ages far more slowly than the one being opened daily, so you effectively get two week-one jars a month instead of one jar with a good half and a bad third. That single change fixed this for me and it costs nothing.

A day or two on the counter is a lot in summer. That alone can move week three to week two.

The other half of the answer is to stop treating week three as failure, because in a Korean kitchen it is not - sour kimchi is its own ingredient with its own uses, and there is a reason those dishes exist.

It is what you want for a kimchi stew, for fried rice, for pancakes, and for anything where it is going to be cooked in fat. Heat and fat round off the sharpness completely, and young kimchi is actually the wrong choice for those - it goes flat and loses what made it good raw.

So the version of your problem I would aim at: make a jar a month as you do, eat the first half raw, and plan the second half as cooking kimchi rather than discovering it as a disappointment. Deliberately keeping some until it is properly sour is a thing people do on purpose.

If you want the raw window to last longer, everything the others said applies. But you are also throwing away the good half of a different ingredient.