In virtual environments, the space that can be explored by real walking is limited by the size of the tracked area. To enable unimpeded walking through large virtual spaces in small real-world surroundings, redirection techniques are used. These unnoticeably manipulate the user's virtual walking trajectory. It is important to know how strongly such techniques can be applied without the user noticing the manipulation - or getting cybersick. Previously, this was estimated by measuring a detection threshold (DT) in highly-controlled psychophysical studies, which experimentally isolate the effect but do not aim for perceived immersion in the context of VR applications. While these studies suggest that only relatively low degrees of manipulation are tolerable, we claim that, besides establishing detection thresholds, it is important to know when the user's immersion breaks. We hypothesize that the degree of unnoticed manipulation is significantly different from the detection threshold when the user is immersed in a task. We conducted three studies: a) to devise an experimental paradigm to measure the threshold of limited immersion (TLI), b) to measure the TLI for slowly decreasing and increasing rotation gains, and c) to establish a baseline of cybersickness for our experimental setup. For rotation gains greater than 1.0, we found that immersion breaks quite late after the gain is detectable. However, for gains lesser than 1.0, some users reported a break of immersion even before established detection thresholds were reached. Apparently, the developed metric measures an additional quality of user experience. This article contributes to the development of effective spatial compression methods by utilizing the break of immersion as a benchmark for redirection techniques.