React Router v4 returning 404 on refresh

I've got a couple of routes defined, and both work, but only when you follow the flow of the app. Let me explain:

We go to the /first page, and the page renders: a bunch of links to the /second/:id page. You click one of the links and the /second/myID page appears.

OK, so far it's all good.

But then I make a change to the code and in the console I get this error: GET http://localhost:8081/second/dist/bundle.js

And the network tab shows bundle.js as a 404. If I refresh the page, I get the same weird /second/dist/bundle.js 404.

If I hit the back button, the URL changes to http://localhost:8081/first, but the page won't appear. If I refresh here, the page shows up properly.

Here's my index.js:

class App extends React.Component {
    render() {
        return (
            <BrowserRouter>
                <div>
                    <Route exact path="/" component={Main} />
                    <Route path="/first" 
                        render={ () => <First 
                                idCards={idCards}
                            /> 
                        } 
                    />
                    <Route path="/second/:id"
                        render={ ({match}) => {
                                return (<Second 
                                    id={match.params.id}
                                />);
                            }
                        } 
                    />
                </div>
            </BrowserRouter>
        );
    }
}

Here's my First component:

export default class First extends React.Component {

    render() {
        return (
            <div className="first">
                {this.props.idCards.map((card, index) => (
                    <Second key={index} {...card} />
                ))}
            </div>
        );
    }
};

Here's the Second component:

export default class Second extends React.Component {
    render() {
        return (
            <h1>{`ID: '${this.props.id}'`}</h1>
        );
    }
}

And my webpack.config.js:

var path = require('path');

const DEV = process.env.NODE_ENV === 'dev';
const PROD = process.env.NODE_ENV === 'prod';

module.exports = {
    devtool: 'source-map',
    entry: './src/index.js',
    module: {
        loaders: [{
            test: /\.js$/,
            loaders: ['babel-loader'],
            exclude: /node_modules/
        },{
            test: /\.(png|jpg|gif)$/,
            loaders: ['url-loader'],
            exclude: /node_modules/
        },{
            test: /\.(css|sass|scss)$/,
            use: ['style-loader', 'css-loader?importLoaders=2', 'sass-loader'],
            // exclude: /node_modules/
        },{
            test: /\.(svg)$/,
            use: ['file-loader'],
            // exclude: /node_modules/
        },
        {
            test: /\.(otf)(\?.*)?$/,
            loader: 'url-loader?limit=10000&mimetype=application/font-sfnt'
        }]
    },
    output: {
        path: path.join(__dirname, 'dist'),
        publicPath: '/dist/',
        filename: 'bundle.js'
    }
}

And my question: Why am I getting this weird request for /second/dist/bundle.js?

It's most likely an issue with relative paths in your index.html file for bundle.js. It works on the home page, because you are already at the root url: /. But when you refresh on a different page, it thinks that it's at the root and that's why you are getting the 404. It's most likely looking for bundle.js at localhost/second/dist instead of localhost/dist.