It depends why they are abusive in the first place.
It is also very rare. Read the book Why Does He Do That - it's written by a man who runs abuser programs. He said the programs have a 10% or less success rate.
The reasons why abusers abuse are very complex but boil down to this - violence is not an aberration or an anomaly of the human condition. Every single one of us could and would be violent given the right circumstances. Imagine fighting for your life - or your DC's life. In normal circumstances it would take extreme fear, rage, desperation and so on before a person would become violent.
Violence happens in a relationship context because EITHER
The abuser has an overgeneralised violent response and reacts disproportionately with violence to a situation which is not so desperate - usually because they have lived with violence for a long time and learned it as a survival mechanism or simply sees it as a normal, standard response. They have learned violence as acceptable. Or sometimes they might have a mental health condition which causes problems with inhibition or the way they experience and/or manage emotions.
and/or
The abuser experiences ordinary relationship events as disproportionate to what they are and experiences the extreme fear, desperation and so on necessary to incite violence. Usually because they have a skewed world view of what relationships are and often based in sexism, although of course relationship abuse sometimes occurs across or against gender norms in the case of same sex relationships or female on male abuse. This abuser greatly fears losing control and sees violence/fear as being their only choice to regain control. Almost ALL abusers have this problem even if they are never actually violent as it is the basis of coercive control. It is very very hard to educate somebody out of this mindset - but it's what abuser programs attempt to do.
Occasionally the misinterpretation of events can be caused by a mental health issue rather than a skewed world view.
or
They are a psychopath, they get pleasure from manipulating and hurting people. This one is extremely rare but also extremely dangerous.
If the sole cause is a mental health issue and it can be safely managed then this will sometimes solve the issues causing the abuse but beware - in some people it will simply never be able to be fully managed and they will never be safe to stay in a relationship with. They would need to be very self aware (which is often difficult). It's also important to be aware that even if a person seems to have changed in every other context, returning to a relationship with a person they have abused can bring about triggers for them which lead back into abusive behaviour patterns once more.
I don't think it's impossible for somebody to change, and if you've been living with your DH for several years following the sincere change then it sounds like it has worked for him and I'm glad for you, really, but it is important to be realistic and admit that the majority of abusers will not (often don't really want to) change. And that for somebody to change does take a long time and you can't assess that it has been successful after living with them for a few months. Sadly a lot of people fall for the tempting belief that they can/have/will and often in an implausibly short time and sometimes it can have dreadful consequences.