What's the advice for dealing with an abusive partner?

I think the texts are ambiguous -- they generally have advice which ranges from, "there's no fellowship with a fool", to, "it can be great if the partners are equal and/or well-behaved and living in tune", to, "your morality (including e.g. good-will) should be unconditional".

If the "abuser" can't solve the issue then in my experience that requires external intervention (e.g. a doctor or psychiatrist), and/or a change in the situation or relationship or the way in which the couple communicates (e.g. relationship counsellor or therapist of some sort), and/or possibly divorce lawyers.

If it isn't psychiatric then consider it may be a psychological problem, like post-traumatic stress.

If the problem persists perhaps the partners suffer from learned helplessness ...

Over the past few decades, neuroscience has provided insight into learned helplessness and shown that the original theory actually had it backwards: the brain's default state is to assume that control is not present, and the presence of "helpfulness" is what is actually learned.

... or perhaps "ignorance" about how to solve it -- so do, try to find help if you can't solve it.

I also suggest you might think it's the other person's problem ("they're the abuser who misbehaves, I am the victim") but when you're in a relationship it's not that simple -- if you went to Al-Anon/Alateen meetings for example you might hear how the behaviour of the family permits or cooperates with the continued misbehaviour.

A counsellor might provide some neutral ground and ensure that both parties are listened to.

A separation (a least a temporary or trial one) might be an option, to explore or consider -- or even just a holiday -- or some other agreement, perhaps a renegotiation of fundamental premises (like "who is expected to do what, and when?"), which a counsellor might suggest.

Beware that people have limits -- if one person is so stressed that they behave irrationally, the other partner too might be vulnerable (to stress and irrationality and abusive behaviour) even if to a different extent/manifestation.

Being too generous or permissive of bad behaviour might be harmful, a teacher (or a paid counsellor) might help to assess if you're going too far.

Unconditional love might in the end be the greatest thing -- or perhaps it's foolish -- who knows, perhaps it's up to you.

1. Mind precedes all mental states. Mind is their chief; they are all mind-wrought. If with an impure mind a person speaks or acts suffering follows him like the wheel that follows the foot of the ox.
2. Mind precedes all mental states. Mind is their chief; they are all mind-wrought. If with a pure mind a person speaks or acts happiness follows him like his never-departing shadow.
3. "He abused me, he struck me, he overpowered me, he robbed me." Those who harbor such thoughts do not still their hatred.
4. "He abused me, he struck me, he overpowered me, he robbed me." Those who do not harbor such thoughts still their hatred.
5. Hatred is never appeased by hatred in this world. By non-hatred alone is hatred appeased. This is a law eternal.
6. There are those who do not realize that one day we all must die. But those who do realize this settle their quarrels.

This might be relevant to your question too -- Reconciliation, Right & Wrong -- and might match some of the things I suggested, e.g. ...

A monk seeking reconciliation with a lay person follows a similar pattern, with another monk, on friendly terms with the lay person, acting as mediator.

... suggests that having a third-person neutral/friendly counsellor might help to repair a relationship.

In the Sujāta-sutta the Buddha speaks of seven types of wives, The first three kinds are heading for unhappiness in this life and the next the last 4 are heading for happiness in this life or the next. The same can be said for the male spouse.

When someone is doing something to you it is almost always because of something you have done previously in this life or earlier. Therefore if you don't patiently tolerate all the abuse hurled towards you the bad kamma won't be extinguished as you are creating more kamma. This just leads to an infinite cycle where you will always be with someone who is abusive in a lot of births.

Best course of action would either be to tolerate everything that keeps happening or you somehow find a way to break off from the relationship without hurting your partner.