Borscht stores well and often tastes better the next day as the flavors meld together. Store it in an airtight container in the refrigerator for up to 1 week. My favorite storage containers for longer lasting fresh food are these mason jars & lids. You can also freeze borscht for up to 3 months. You can also freeze borscht for up to 3 months; just thaw it in the refrigerator overnight before reheating.