Gamma-ray bursts (GRBs) are the most luminous transient events in the Universe, and as such are associated with some of the most extreme processes in nature. They come in two types: long and short, nominally separated either side of a two second divide in gamma-ray emission duration. The short class (those with durations of less than two seconds) are believed to be due to the merger of two compact objects, most likely neutron stars. Within this population, a small subsection exhibit an apparent extra high-energy emission feature, which rises to prominence several seconds after the initial emission event. These are the extended emission (EE) bursts. This thesis investigates the progenitors of the EE sample, including what drives them, and where they fit in the broader context of short GRBs. The science chapters outline a rigorous test of the magnetar model, in which the compact object merger results in a massive, rapidly-rotating neutron star with an extremely strong magnetic field. The motivation for this central engine is the late-time plateaux seen in some short and EE GRBs, which can be interpreted as energy injection from a long-lived central engine, in this case from the magnetar as it loses angular momentum along open field lines. Chapter 2 addresses the energy budget of such a system, including whether the EE component is consistent with the rotational energy reservoir of a millisecond neutron star, and the implications the model has for the physical properties of the underlying magnetar. Chapter 3 proposes a potential mechanism by which EE may arise, and how both classes may be born within the framework of a single central engine. Chapter 4 addresses the broadband signature of both short and EE GRBs, and provides some observational tests that can be used to either support or contradict the model.