Imagine yourself to be bat. You cant see anything. You don't have eyes. All you can do is echolocate, using ultrasound. Now imagine something is moving away from you faster than the speed of sound. Can you locate it ? Can you perceive its existence ? If the answer is yes, how ? If no , then from the bats perspective it should be highest speed that can be achieved . Then how can we, as humans say that speed of light is maximum in the universe because we wont be able to detect anything moving faster than speed of light.
Bats can still feel things.
Although they cannot hear something that is moving away faster than the speed of light, the movement still has physical consequences, even to the bat.
Given adequate measurement tools and the ability to understand and operate them, a bat could still detect things moving faster than the speed of sound, even if it could not use echolocation on them; because there is still information about the event that is transmitted in some way.
On the other hand, we cannot find any significant evidence of movement faster than the speed of light.
Bats live in a world where things can still be detected travelling faster than sound.
Neither bats nor us live in a world where things can still be detected when travelling faster than light. This provides us with plenty of evidence that the speed of light in a vacuum is an actual limit; not just an artifact of our perception.
There is plenty of experimental evidence that objects can move faster than the speed of sound but no evidence they can go faster than light.
We hold that $c$ is the ultimate velocity not because we don't have the appropriate apparatus to measure speeds greater than $c$ (indeed there was actually rumours few years ago that some superluminal neutrinos had been detected) but because assuming $c$ is the ultimate velocity has lead to predictions validated by a multiplicity of experiments. Examples include muon decay experiments, high energy physics experiments including effects of Thomas precession etc.
Assuming that $c$ is not only the ultimate speed but also an invariant (i.e. the same for any two inertial observers) allows us to deduce Lorentz transformations, which allow us in turn to understand, for instance, deep connections between electric and magnetic fields. One can also show that faster-than-light signals lead to contradiction in causality.
Special relativity, which hinges on the invariance of $c$, is also the stepping stone to general relativity, which predicted the recently detected gravitational waves.
In other words, while there is no experimental challenge to this assumption, the consequences of this assumption lead to very rich physics which has been experimentally verified.
An important point was missed here - the bat analogy fails much more quickly than others realize.
An object that travels faster than the speed of sound still can emit sound and reflect sound from other sources. The same would be true of a FTL particle, unless it's completely non-interactive (see Russell's teapot).