There are several factors which determine how fast instant glue will dry. A common reason for CA glue not drying is that the glue being used is too thin for the joint. If CA glue is not being pressed between two surfaces and has not had accelerator applied, it will take a long time to cure, and if the glue is too thin for the application, it will still not create a bond when it does cure.
Another factor in curing time is the material being bonded. Different substrates cause instant glue to dry at different speeds. When bonding rubber or neoprene, for example, the glue will dry extremely quickly, while materials such as polycarbonate tend to take a bit longer.
Oils and other contamination on the surfaces can cause the glue to bond slowly, weakly, or not at all. Lack of humidity in the air can also affect curing times. Alsom, the more instant glue that is used in a given bond area, the slower the cure will be.