Yes Cyclamen plants do come back every year so when they die out they will regrow the next season.
The Cyclamen plant which is a tuberous perennial and will come back every year and they do best in warmer climates but you can still plant them in colder climates as long as you're able to protect the Cyclamen Plant from the frost or cold weather.
In Colder Climates especially in Zone 6 you should add an extra layer of mulch to protect the Cyclamen Plant from harsh temperatures during the winter.
In doing so the Cyclamen Plants should come back every single year as long as you take care of them.