Forget Me Not flowers can actually be both annuals and perennials depending on the species of the Forget Me Not flowers because there are actually a few different species of the Forget Me Not Flowers.
You'll certainly see your Forget Me Not Flowers come back every year in the spring if they do happen to die out in the winter.
So if you have outdoor Forget Me Not Flowers they'll usually die off in the winter and then once spring comes back the Forget Me Not Flowers will almost always return.
That's what happens to a few of my Forget Me Not Flowers that are outdoors.