Yes, they can however varicose veins are very unlikely to occur if they are treated correctly in the first place and there is a suitable time for ongoing surveillance (1 – 2 years). Spider veins will almost always return to some extent for the same reason that they occurred in the first place – genetics! The interval between treatments is determined by many factors including the severity of the condition, age of the patient and number of pregnancies etc. but as a guide, a forty-year-old woman should expect to get 5-7 years from Sclerotherapy (if done properly with reticular veins also treated) before she feels the need for further treatment.