Is walking away from the situation then not bringing it back up again considered running away from your problems?

Many times I’ve accused my lover of running away from problems, because of the way we handle arguments: When we are arguing, I strive to turn the argument away from being a blame game, instead turning it into an intelligent discussion so that we can solve the problem. She, on the other hand, doesn’t want anything to do with discussions, and instead leaves the house until she is cooled down. This would be fine with me if she came back ready to fix the issue, but instead she comes home as if everything has been resolved and gets mad if I try to talk to her about it. The annoyance of the issue still lingers with me, because it hasn’t been resolved, so it starts the pattern over again a few days later.

So, as I said, I’ve accused her of running away from her problems, and she’s actually acknowledged that she has a problem with that, and she has been doing it since she was a kid.

Today, though, after fighting with her on and off all day, we got into the whole blaming phase where I’m telling her off for leaving shit all over the place for me to clean and she’s telling me off because she “works all day” and is tired when she gets home, and when it got to the point where she told me to shut up about it and basically told me to go away, I took a shower and I left. I told her I was going look for our dog (who has been missing for a couple of hours), but after driving around the apartments for a little bit I abandoned the search and went to my mom’s house to take a breather outside by the pool and smoke a couple of cigarettes.

By the time I came home, I was over it. It was slightly different from the way my girlfriend does it, because I didn’t refuse to talk about the problem – but she didn’t try to talk about it. She said sorry, I said sorry, and there’s still shit all over the house and she still works all day and is tired when she gets home, but I just don’t even want to have the stress of talking about it anymore.

So, is walking away from an argument and never talking intelligently about the issue actually just running away from the problem, or is it sometimes just a necessary part of human nature to keep us from violence? Or am I thinking too deep into this, and it’s not really that big of an issue? What are some better ways to deal with arguments when it gets to the point of a childish blame game, but neither of us are ready to back down? And where the hell is my dog?