The only confirmed phenomenom that involves something occurring faster than the speed of light that I'm aware of is the apparent instantaneous communication involved in quantum entanglement. However, since this does not involve actual movement and the mechanism for the correlation between the entangled pair is unknown, I'm not sure if this is grounds for disqualifying relativity.
We've known for a while that relativity is not a complete theory, as there are parts of quantum physics that contradict it. However, relativity still accurately describes the behaviour of many observable phenomena, and much of modern technology is based around it. That's why people "defend" it: just because it isn't universally applicable doesn't make it useless. Similarly, people still use Newton's laws even though relativity superceeds them. When dealing with normal object moving at normal speeds, Newton is still good enough.
Finally! Someone mentions "Spooky Action at a Distance".
Space/Time deformation can effectively exceed the speed of light. That is supposed to explain the 'mechanism' of 'entangled' charged particles, the deformation of space/time. They cheat and change the playing field.
Now when are those who can reconcile dark energy/matter with this puzzle going to do so?