How long will white miso keep after opened and refrigerated?
Cover it with plastic wrap and press down to prevent air contact. Contact with air is the only thing that can make 'go bad' and usually that's just a surface layer that's dried out. So keep it sealed from air.
Miso is amazingly stable in the 'fridge. In fact some would say years. I've had brown miso in the 'fridge for more than a year and it's still good, it won't mold or go bad, it's like honey in that respect. Just press down some plastic wrap or wax paper on the top of it after using to limit air contact and drying it'll be good for ages.
White miso is less salted than red(dark brown) miso, so in the aspect of keeping it will change the taste and flavore faster than red miso. Japanese cares its freshness, so even if miso is preserved food and keeps well, we try to use up as fast as possible, say less than one month. Along with the color change, the taste change and this aging is not always nice. (but if your miso is homemade, the aging is necessary and it is another story)