The inferior long-term stability of polymer-based solar cells needs to be overcome for their commercialization to be viable. In particular, an abrupt decrease in performance during initial device operation, the so-called 'burn-in' loss, has been a major contributor to the short lifetime of polymer solar cells, fundamentally impeding polymer-based photovoltaic technology. In this study, we demonstrate polymer solar cells with significantly improved lifetime, in which an initial burn-in loss is substantially reduced. By isolating trap-embedded components from pristine photoactive polymers based on the unimodality of molecular weight distributions, we are able to selectively extract a trap-free, high-molecular-weight component. The resulting polymer component exhibits enhanced power conversion efficiency and long-term stability without abrupt initial burn-in degradation. Our discovery suggests a promising possibility for commercial viability of polymer-based photovoltaics towards real solar cell applications.