In The Fridge: If you store any leftover Brussels sprouts in an airtight container in the refrigerator without mixing the sriracha sauce, they will stay fresh for another three to four days.. In The Freezer: Completely let the Brussels sprouts cool. Place the cooled sprouts in freezer-safe sealed containers or bags. Crispy sprouts can be frozen for up to 4 months with a name and date labeled on them.