Unsupervised neural machine translation (UNMT) that relies solely on massive monolingual corpora has achieved remarkable results in several translation tasks. However, in real-world scenarios, massive monolingual corpora do not exist for some extremely low-resource languages such as Estonian, and UNMT systems usually perform poorly when there is not adequate training corpus for one language. In this paper, we first define and analyze the unbalanced training data scenario for UNMT. Based on this scenario, we propose UNMT self-training mechanisms to train a robust UNMT system and improve its performance in this case. Experimental results on several language pairs show that the proposed methods substantially outperform conventional UNMT systems.