No, not normal for someone who wants to reconcile!

Sam Sam -- No, it's not normal for someone who wants to reconcile. This is normal for an unfaithful spouse who takes no responsibility for her choices, nor for her spouse's suffering. There are many articles here in AffairRecovery for the necessary steps for both parties to take if reconciliation is possible (I know, I've read just about all of them). What she's doing shows she is not committed to your marriage. My wife (the unfaithful) is similar, 2 1/2 years after DDay and she is only about 1/10 the way through telling me the truth -- a new revelation every few months.

The solution (in my mind, and according to several articles here) is to set clear and firm "Boundaries". Each is a statement of what you expect for the relationship to be repaired and commitment to be genuine. And state what will happen if the boundaries are not respected. Then, it's her choice whether she takes the consequences.