No, they should not. If varicose veins are closed correctly, there is less than 1% chance that those specific treatments (i.e. treated veins) will fail over time. However, there is always a possibility that additional veins will become abnormal as time progresses. Venous disease is a chronic progressive disease process. The time frame varies from person to person, and is predicated upon family history and contribution of other risk factors.
It's important to seek treatment if you are symptomatic with leg pain, leg fullness, and non-specific heaviness in the legs, especially after standing for long periods of time. Finally, if you have a history of chronic venous insufficiency, consider evaluation annual or every few years regardless of symptoms in order to keep your venous insufficiency under control.