Code clones are the same or nearly similar code fragments in a software system's code-base. While the existing studies have extensively studied regular code clones in software systems, micro-clones have been mostly ignored. Although an existing study investigated consistent changes in exact micro-clones, near-miss micro-clones have never been investigated. In our study, we investigate the importance of near-miss micro-clones in software evolution and maintenance by automatically detecting and analyzing the consistent updates that they experienced during the whole period of evolution of our subject systems. We compare the consistent co-change tendency of near-miss micro-clones with that of exact micro-clones and regular code clones. According to our investigation on thousands of revisions of six open-source subject systems written in two different programming languages, near-miss micro-clones have a significantly higher tendency of experiencing consistent updates compared to exact micro-clones and regular (both exact and near-miss) code clones. Consistent updates in near-miss micro-clones have a high tendency of being related with bug-fixes. Moreover, the percentage of commit operations where near-miss micro-clones experience consistent updates is considerably higher than that of regular clones and exact micro-clones. We finally observe that near-miss micro-clones staying in close proximity to each other have a high tendency of experiencing consistent updates. Our research implies that near-miss micro-clones should be considered equally important as of regular clones and exact micro-clones when making clone management decisions.