The physical processes or trigger mechanisms that lead to the eruption of coronal mass ejections (CMEs), the largest eruptive phenomenon in the heliosphere, are still undetermined. Low-altitude magnetic reconnection associated with flux cancellation appears to play an important role in CME occurrence as it can form an eruptive configuration and reduce the magnetic flux that contributes to the overlying, stabilising field. We conduct the first comprehensive study of 20 small bipolar active regions in order to probe the role of flux cancellation as an eruption trigger mechanism. We categorise eruptions from the bipolar regions into three types related to location and find that the type of eruption produced depends on the evolutionary stage of the active region. In addition we find that active regions that form eruptive structures by flux cancellation (low-altitude reconnection) had, on average, lower flux cancellation rates than the active region sample as a whole. Therefore, while flux cancellation plays a key role, by itself it is insufficient for the production of an eruption. The results support that although flux cancellation in a sheared arcade may be able to build an eruptive configuration, a successful eruption depends upon the removal of sufficient overlying and stabilising field. Convergence of the bipole polarities also appears to be present in regions that produce an eruption. These findings have important implications for understanding the physical processes that occur on our Sun in relation to CMEs and for space weather forecasting.