It really depends on the mithai you're enjoying. Most Asian and Indian sweets can be kept in the fridge, but for best freshness consume within two to three days.
Though we recommend to transfer them from the classic cardboard box into a glass container to keep them as fresh as possible.
Ghee Indian sweets dipped in sugar syrup:
Like sooji halwa, laddu or jalebi can be kept out of the fridge in winter and eaten within 6-8 days or 15 days if kept in the fridge.
Dipped in sugar syrup:
Like gulab jamun and rasgulla should be eaten as soon as possible in the summer (which is pretty easy, since they're super tasty), but are good for about four days when kept cool.
Khoya Indian sweets:
Like peda and barfi stay fresh for a good few days due to how the khoya is roasted. You can keep them fresh in the fridge for 7-10 days.
Milk-based Asian and Indian desserts:
Like ras malai or kheer should be consumed within one to two days and refrigerated.