I love kim chee, but I can't always get up to the Asian market, so when I do, I buy a half-gallon of kim chee.
I immediately transfer it to smaller glass jars, which I fill up to the top. When you get down to the last jar, you may have to add some water.
When I eat some of the kim chee and it then does not fill up the container, I transfer it to a smaller container, so it will fill the container to the very top.
I've now tried this with 3 half-gallons of kim chee that I've bought, and this has stretched over 2 months. Your kim chee will not become sour if you do this. The reason is that the sour taste comes from fermenting in oxygen, and kim chee is fermented without oxygen (different bacteria).