How to prolong the life of chillies in a refrigerator?
Per Still Tasty, the shelf life of chili peppers is only going to be about a week.  You were probably simply unlucky in having them turn more quickly than that.

In general, this type of chili is not eaten raw, and featured for its texture, so freezing should in fact be a very good option, despite slight degradation in texture that may occur.

Depending on your planned use, you may also consider making refrigerator pickles which will allow them to last several weeks or more refrigerated, but will give them of course and acidic and pickled flavor.