In order to controllably grow single-wall carbon nanotubes (SWCNTs), a better understanding of the growth processes and how they are influenced by external parameters such as catalyst and gaseous environment is required. Here, we present direct evidence of growth termination of individual SWCNTs and successive growth of additional SWCNTs on Co catalyst particles supported on MgO by means of environmental transmission electron microscopy. Such in situ observations reveal the plethora of solid carbon formations at the local scale while it is happening and thereby elucidate the multitude of configurations resulting from identical external synthesis conditions, which should be considered in the quest for controlled SWCNT growth. Using CO and a mixture of CO and H2 as carbon sources, we show that the growth of SWCNTs terminates with a reduced tube-catalyst adhesion strength. Two main reasons for the cessation are proposed: insufficient active carbon species and a certain amount of stress exerted at the tube-catalyst interface. Interestingly, it was observed that catalyst particles stayed active in terms of nucleating additional solid carbon structures after growth termination of the first SWCNT. These observations elucidate the importance of an in-depth understanding of the role of catalysts and carbon sources in the continued growth of SWCNTs. Furthermore, it serves as a guide for further control of carbon nanostructure synthesis via catalyst engineering and synthesis optimization.