Subjects who are evaluated on Day 42 (Week 6) as Responders from either Treatment Phase I or Treatment Phase II will continue through into the 46-Week, Long-Term Extension Phase III of the study, and be monitored and assessed by phone for RLS symptoms (IRLSS and Hopkins RLS-Sleep Quality Questionnaire [HRSQ]) and adverse events on (approximately every 9 weeks) Weeks 15, 25, 34, 43 and 52 (final follow-up visit). During Phase III subjects may receive additional unblinded treatments with FCM if at any time the subject reports worsening of RLS symptoms (an increase >4 points on the IRLSS compared to the last evaluation captured for that subject) and laboratory criteria are met (ferritin <300 ng/mL and a TSAT <45%). Subjects will receive a single FCM 750 mg undiluted slow IV push at 100 mg/minute. See section 6.6 for dosing and assessment outline. No additional treatment will be allowed after the Week 46. A final face-to-face study visit will occur on Week 52 (approximately 365 days since initial Day 0 Treatment). If a clinic visit is not possible, final evaluation will be completed by phone.