In Wassertein GAN, the discriminator does not really play the role of a critic between the real and fake image samples. Instead, it is providing a way to estimate the difference in distribution of real and fake samples.
And it is expected that the discriminator loss decreases over time. But if keeps on decreasing, I suspect that the weights are not clamped. So, you may want to clip the weights of the discriminator within a small range like [-0.01, 0.01] after each update applied to the weights of the discriminator.
Also, this blog-post very nicely describes the Wasserstein distance: https://lilianweng.github.io/lil-log/2017/08/20/from-GAN-to-WGAN.html 63