Is sublimation caused by an environmental difference or an element's composition?
To a first approximation, any pure substance can sublimate. However, complex substances may decompose or change their structure before any appropriate sublimation conditions are reached.

The only (and very remarkable) exception is helium (in fact, helium is so special that helium-3 and helium-4 have quite different phase diagrams even though they're isotopes!). Note that due to the presence of superfluid phases, there is no direct transition between the solid and gas phases in either isotope.

As an aside, there is nothing prohibiting a substance to exhibit a solid-gas transition curve crossing a region of mild temperature and pressure conditions. Though unusual, an interesting example is iodine heptafluoride. It has a very narrow liquid range at ambient pressures (meaning a small decrease in pressure is enough to go below the triple point pressure), and the liquid range happens to fall near very reasonable temperatures.