Why was Persephone not permitted to leave Hades permanently?

Because he wanted her to be his wife forever.

Persephone was abducted by Hades to be his wife. She wasn't supposed to eat anything in the land of the dead, but Hades gave her a pomegranate. She ate some seeds (I forget how many - legend said 1/4 of the pomegranate. Demeter, her mother, goddess of crops/earth/growing things was so distraught over the loss of her daughter she hid herself from the world. Zeus got panicky because the world fell barren while Demeter wasn't there, crops didn't grow, etc. so he bargained with Hades to get Persephone back to the living world. Because she'd eaten the food of the dead, she was only allowed to return for a period of time, then return for a period of time. This explains why we have spring and summer, when she's back from the land of the dead, and fall and winter, when she's back with Hades. Actually, the 1/3 pomegranate only accounts for winter (1/3 of the year) but some legends include fall as well as part of the time she's downstairs.