I've been having this issue for awhile now, first describe here. After upgrading to Webpack 4, it seemed like the issue resolved itself, but it doesn't seem to be the case.
The issue here, is that after deploy, when the chunks get updated, the server is not aware of it? It's quite hard to reproduce this issue and I never were able to do it on demand. But sometimes, if I have the page hanging, the browser will try to grab, what I assume, cached versions of webpack chunks for css and js. But as those are outdated now, I end up with this and a empty website:
Reloading the page, sometimes having to do a force reload, is the only way to fix this, as browser redownload the correct chunks. I'd love to get some pointers to resolve this, as I've never managed to find anything written on this and how to fix this. I am planning to either drop chunks all together or provide an inline JS that will ask to reload the page if it detects any of these 404s... which is not ideal way to do this.
You can find my webpack configuration in the link above. I am deploying this to Heroku, my app is Rails 5.1, with Vue.js 2