We haven’t heard of many people with Touch ID issues, but we don’t know many people with an iPhone 5S, either.
However, it seems that some are experiencing problems with Touch ID “fading.” While people are trying to use the touch sensor on their handset, it’s quality seems to diminish over time. Some say they have to rescan their fingerprints. Even then, they eventually have to rescan again.
That said, Apple and the team that developed the technology are working to improve its functionality with a software fix in the near future. According to the report, it’s not clear if that’s coming with iOS 7.1, or at a later date.