"she cannot bring herself to the final step of rejecting all the Suitors or accepting one of them"

Women in ancient Greece needed men to provide for them. Although a widow might return to her father’s household or rely on brothers to look after her, this would be far from the ideal situation. The best thing Penelope could do if Odysseus were truly dead would be to re-marry. However, her love for Odysseus prevents her from taking these steps while she can still hold even a slim hope of his being alive.