Leaving aside the question of what constitutes suffering, I think the look for the cause of suffering needs to be split into two activities. We need to look at the proximate (direct/immediate) cause and the ultimate (overall/initial) causes of suffering.
The proximate cause of suffering can probably be defined in neurochemical terms by an imbalance of certain chemicals in the brain. It may be that we even find this to be the most useful way of defining the existence of suffering. This is a relatively easy question and I imagine that this this will be answered soon if it hasn't been already.
The ultimate cause however may involve some conjecture as it is likely to have both evolutionary and environmental components. A basic description of how it may have happened is this: At some point in our evolution there were two types of human brain, the chemistry in brain 'A' improved the accuracy of identifying smells and allowed those with brain 'A' to be better at identifying predators and therefore escaping from them. This gave 'A' brainers an evolutionary advantage over 'B' brainers as they were more likely to reach sexual maturity and reproduce. This in turn meant that the genes for an 'A' brain became more prevalent as they were passed on from 'A' parents until 'A' became the dominant kind of brain in humans. now it may be that the same gene combination that improved smell in 'A' brainers also caused an increase in the production of the protein "sufferon" (my invention), the chemical which is the proximate cause of suffering. it is also likely that the effect of "Sufferon" is magnified or ameliorated by certain environmental factors and these then form part of the ultimate cause.
This sort of explanation may not be as satisfying as religious, emotional or psychological explanations (what's the chemical for satisfaction ;-). However I believe it is more likely to lead to a better understanding of human feelings, emotions and behaviour and possibly the alleviation of suffering itself if that is what we aim for.