They die back each year but don't return.
How Do I Make My Sweet Peas Hardy
Certified GKH Gardening Expert
It sounds as if you may be growing the annual sweet pea variety rather than the perennial, which returns each year. Make sure you are growing the right one. If you are growing the perennial variety (Lathyrus latifolius), they will reseed themselves each year. Lathyrus odoratus is the annual type.