What factors tend to be common in cultures with widespread institutionalized slavery? For example, I know that a demand for cheap labor is a factor, like with the slaves in the American South farming cotton after the cotton gin was invented, but what else needs to be considered?
Demand for cheap labor, which you already mentioned, is one factor.
The other factor is the absence of "Human rights" concept, or very limited viewing of it. In XIX century western society, it has long become unacceptable to have white slaves. However, people of different color were viewed differently, and it was accepted that their rights are different.
There are more factors, like wars, which provide a stream of new slaves for the economy. In second century AD Roman conquests have reached their peak. That meant that the supply of slaves had become limited, which turned out one of the critical reasons for the Ancient Rome to decline and eventually fall.
Lack of automation: if you can get a machine to do it you probably won't use slaves, since machines are often cheaper & better (Espacily in the long run) this may also take the form of a volatile economy in which the upfront cost of automating a process is not worth the risk of that process no longer being needed.
Lack of morality: this might be high and mighty of me but slavery is not a system that should be used, like ever. Any civilization that practice's it is missing the ability to see someone as human. Common examples are the triangular slave trade and Nazi prison camps.
Low education threshold for work: in general slavery works better for 'uneducated' labour as its easier to make someone work when you can clearly see a measure of it 100 acres of land ploughed vs 100 programming done(?).
Non-chatel slavery systems: slavery doesn't have to mean whips, chains and farm hands for instance The Ottoman empires jannisaries were a form of slave and broader definitions of slavery can exist under different conditions.