ARM I: Patients receive ziv-aflibercept IV over 1 hour on day 1 and topotecan hydrochloride IV over 30 minutes on days 1, 8, and 15. Treatment repeats every 21 days for 4 courses in the absence of disease progression or unacceptable toxicity. Patients with responsive or stable disease after 4 courses may then receive ziv-aflibercept IV on day 1 and topotecan hydrochloride IV on days 1 and 8. Treatment repeats every 21 days in the absence of disease progression or unacceptable toxicity.