The article describes forgetting as overlapping with denial in the "I never said that" category. The abuser will "forget" that he or she did, in fact, say that. Or, the abuser will "forget" a promise he or she made.

My current husband has a problem here too. I can ask him to do something I'm unable to do myself, and he'll say, "Sure, I'll get to it." Days or even weeks may pass, and it's still undone. When I remind him, "Oh, yeah, I forgot." Message, "I didn't care enough to bother trying to remember." If I'm very upset that what I asked for was forgotten, "Well, why didn't you remind me?" Which, of course, isn't very far from blaming the victim. My therapist didn't let him get away with that. He pointed out to my husband, "If your boss at work tells you to do something, you're not going to shrug it off and let it go for weeks. You're going to get right on it, because it's important. So if your wife wants you to do something, and you agree to it, at what point does it become your responsibility to remember, and not hers to remind you?"

With my ex, he would repeat the same insults over and over, "forgetting" that I asked him not to say that to me because it hurts. A letter appeared in Ann Landers once. A woman wrote that her husband constantly repeats the same two jokes at parties, and both of them hurt her. If he sees her talking to a man, he will say to that man, "Are you trying to steal my wife, you horse thief?" His other favorite line is, "I'd like to die in bed, being shot by a jealous husband." His wife doesn't like these jokes because one calls her a horse, and the other puts him in bed with another woman. Yet he keeps on making them. Ann Landers advised the woman to tell her husband once that the jokes hurt her and she'd like him to stop it. After that, if he does it again, he is abusing her deliberately.

Predictably, my ex responded, "Not necessarily. What if he forgets?" And my point is, if he loves her and cares about her feelings, he won't forget because it will be important to him.

ETA: Just a correction, because sometimes I'm obsessive like that. It was Dear Abby, not Ann Landers. Link here.