All breeds of cats have specific health risks.
Sphynx are a relatively healthy breed. There are some breed specific health issues to be aware of, Hypertrophic Cardiomyopathy, Urticaria Pigmentosa, Periodontal Disease, Hereditary Myopathy, Cutaneous Mastocytosis, as well as other health concerns known to inflict all cats, not just specific to Sphynx.
Responsible breeders DNA test potential breeders for the most common concerns. This can be over 50 different genetic markers. HCM scans should be mandatory. Respiratory PCR, and fecal PCR panels should also be done.
Sphynx can be prone to respiratory issues, yeast or bacteria imbalances in the ear, and sometimes toe pockets. Some can suffer from allergies, and sensitive stomachs.
Not all health issues are hereditary. Screening and clearing prior to breeding greatly reduces the chance of an unhealthy kitten.
Breeding only the healthiest cats will improve the breed.