There are a few caveats to integrating vuex-module-decorators with nuxt. The first steps are described in the README (although I missed it because it nuxt was in the small text).
In addition to this, according to issue #179, there are a few other caveats
drone ah adventures 
I love you so damn much, thank you! I’ve been tackling this bug with Nuxt and vuex-module-decorators for hours but these caveats solved it. These caveats are so subtle (or even non-existant) in the documentation that I would’ve never noticed it if it weren’t for this godly post. If you’re reading this right now, Drone Ah, just know that you’ve saved me tonnes of time and pain, and no matter how much I write in this reply, I could never express how appreciative I am of you and this post!