Yo I know this is just a manga, but your partner being "way too drunk" isn't an excuse. Don't let things drop this easily. It's not "fine." If I saw my friend desperately chasing after someone who struck them and then wave things off with a couple excuses and an apology I'd be crazy worried for them.
Abuse isn't something you just wave away, even when it starts out with something minor. Especially if the person who did it tries to act like it was minor. Or in this case, just cuts off contact for a few days and then makes a bunch of bullshit excuses before finally apologizing