Although each collision at CERN has the available energy to create a Higgs boson each time, the vast majority of the time it does not create one. I suspect that part of the reason for this is that most of the energy goes into creating mostly lighter, secondary particles which carry a lot of kinetic energy away. As a result, this would leave very little energy left to create more massive Higgs bosons.
So I started thinking and realized that there is more that is going on (e.g. cross sections sizes). I have purposely left this question open-ended to just see what people are thinking since I know very little about this. Therefore, as the title of this question puts it: why is the Higgs boson not created more frequently at the CERN collider?
Aside: I guess I could of asked this question about some X-particle instead of the Higgs boson. Either way, my question would still be the same.