Background: The software engineering community has increasingly conducted systematic literature reviews (SLR) as a means to summarize evidence from different studies and bring to light the state of the art of a given research topic. While SLR provide many benefits, they also present several problems with punctual solutions for some of them. However, two main problems still remain: the high time-/effort-consumption nature of SLR and the lack of an effective impact of SLR results in the industry, as initially expected for SLR. Aims: The main goal of this paper is to introduce a new view - which we name Sustainability of SLR - on how to deal with SLR aiming at reducing those problems. Method: We analyzed six reference studies published in the last decade to identify, group, and analyze the SLR problems and their interconnections. Based on such analysis, we proposed the view of Sustainability of SLR that intends to address these problems. Results: The proposed view encompasses three dimensions (social, economic, and technical) that could become SLR more sustainable in the sense that the four major problems and 31 barriers (i.e., possible causes for those problems) that we identified could be mitigated. Conclusions: The view of Sustainability of SLR intends to change the researchers' mindset to mitigate the inherent SLR problems and, as a consequence, achieve sustainable SLR, i.e., those that consume less time/effort to be conducted and updated with useful results for the industry.