What caused Abigail to lose her job with the Proctors? Why won't other people hire her?

Abigail lost her job at the Proctors' because she had an affair with John. The continued presence of Abigail in the household would've created even more instability and tension in the Proctors' marriage, and so Elizabeth had no choice but to let her go. Abigail deeply resents being fired and vows revenge upon Elizabeth. False accusations of witchcraft are a way to get back at her.
No one will hire Abigail because she's starting to get a bad reputation in town. After what she got up to with John Proctor, no self-respecting married woman would want to have someone like under that living under their roof. In a small, God-fearing town like Salem, reputation is everything—as we will see with John Proctor later on in the play—and Abigail's reputation as a home-wrecker means that no one wants to hire her, however good at her job she may be.