Our rabbit-hunting ancestors (Fa et al. 2013)

From the paper:

Relative to other mammal groups, rabbit bone abundance was always significantly higher during the Upper Palaeolithic (76%) and Mesolithic (59%) than during the Middle Palaeolithic (Fig. 4). The difference between the average rabbit remains and that of cervids, the second most abundant prey item, were less than 10% during the Mousterian. In contrast, during the Upper Palaeolithic and Mesolithic, the difference between the rabbit and the second-most important prey items was over 60% and 20%, respectively. After the rabbit, large ungulates (caprids, cervids and equids) were relatively important during the Middle and Upper Palaeolithic, while caprids, cervids and suids took that place during the Mesolithic (Fig. 4).

and:

Our evidence indicates that hominin diets may have changed from one dependent on large mammals during the Middle Palaeolithic to diets dominated by smaller species in the Upper Palaeolithic, in particular by the wild rabbit. The explanation for this transition is either that climate change negatively impacted large mammal populations, forcing prehistoric people to incorporate smaller vertebrate species into their diets, or that people themselves negatively impacted large mammal populations, which in turn forced foragers to add smaller species to their diets. 

I am not sure how modern hunter-gatherers hunt rabbits, but I would think that trapping, or some type of slingshot or blowdart would be ideal for this small and fast-moving animal. Did Neandertals simply lack efficient technology to capture rabbit, or is there some other reason why they underutilized the species?

Journal of Human Evolution DOI: 10.1016/j.jhevol.2013.01.002

Rabbits and hominin survival in Iberia 

John E. Fa et al.

High dependence on the hunting and consumption of large mammals by some hominins may have limited their survival once their preferred quarry became scarce or disappeared. Adaptation to smaller residual prey would have been essential after the many large-bodied species decreased in numbers. We focus on the use of a superabundant species, the rabbit, to demonstrate the importance of this taxon in Iberia as fundamental to predators. We show that the use of the rabbit over time has increased, and that there could have been differential consumption by Neanderthals and Anatomically Modern Humans (AMH). Analysis of bone remains from excavations throughout Iberia show that this lagomorph was a crucial part of the diet of AMH but was relatively unutilised during the Mousterian, when Neanderthals were present. We first present changes in mammalian biomass and mean body mass of mammals over 50,000 years, to illustrate the dramatic loss of large mammalian fauna and to show how the rabbit may have contributed a consistently high proportion of the available game biomass throughout that period. Unlike the Italian Peninsula and other parts of Europe, in Iberia the rabbit has provided a food resource of great importance for predators including hominins. We suggest that hunters that could shift focus to rabbits and other smaller residual fauna, once larger-bodied species decreased in numbers, would have been able to persist. From the evidence presented here, we postulate that Neanderthals may have been less capable of prey-shifting and hence use the high-biomass prey resource provided by the rabbit, to the extent AMH did.

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