I had the show on, but only bits and pieces held my attention.
Abby, alone, is not all that interesting and neither is her life.
She has an immaturity and a vulnerability about her.
We've seen her immaturity again and again, with her lack of self control. Lashing out at people, and especially children, is not a sign of strength, it's a sign one has lost control over their own emotions. And we saw her immaturity again last night by her refusal to fully accept responsibility for her choices and actions. In this particular case, she accepts her punishment... she'll do her time and be done with it, (she has no other choice) but she has not accepted responsibility.
As for her vulnerability, it might be the one thing that keeps her somewhat likable. However, she's vulnerable because she's so immature. She simply has not figured out that a relationship is more than just how SHE feels about someone, it's more importantly, about how she makes THEM feel. She can love this person or that student, etc., but if they don't know they're loved, if they don't feel loved, it's really doesn't matter. I think this is quite evident by her lack of long lasting serious relationships. It seems to me, that she is lonely, and filled with sadness but can not connect it to her own behavior. I hope she will one day learn, but sadly, I feel that won't be the case.
She'll be back, she'll try to stay current and keep relevant, probably somehow try to use all this to her advantage, and a few people may take notice for awhile, but she won't have changed or learned anything.