There are a wide variety of Baby's Breaths. The two most common are Annual Baby's Breath (Gypsophila elegans), and Florist's Baby's Breath (Gypsophila paniculata), though a few others are available from specialists. Annual Baby's Breath, as the name implies, is a half hardy annual, and is not likely to survive the winter. The other species are perennials, and probably should be cut back in early spring. Many are short lived, so you might want to take a few cuttings to keep on in a cold frame or cool greenhouse, to replace older plants.