Okay - one of the main reasons that the response wrt concentration isn't linear to infinity - and the most physically practical, dominating effect -- is simply light scattering. Various non-linear optical effects, which after 14 years in a spectroscopy lab, still holds a black-box explanation to me, are also a contribution in this type of situation is considerably negligable, unless a laser is your light source.
The absorbance/transmittance means of measuring observes the comparision of light that makes it to the detector vs does not make it to the detector , with a linear path between the light source and the detector.
At low concentrations of an absorbing species, a fraction of the light pumped into the sample chamber is indeed "being taken out" by the material in solution, and the rest of the photons travel in the straight line to the detector.
As the concentrations increase at the very low concentrations values, you get a response showing that if you double the amount of absorbing species in that same volume (2x concentation), you get essentially 2x as much of the initial light absorbed, and this continues this way within a low range.
But as the concentrations get higher, you hit the point where the solutes may form nanoparticles, and you'll see Raylegh scattering - Rayleigh scattering also can occur if a solution is not homogenous and has regions where a refractive-index changes, but assuming a nicely soluble, homogenous mixture thats not an issue. Water-thinned milk is a good example of the effect that you can see with your eye, it is tinted blue due to the scattering of particular wavelengths in white light, but those particles (colloids ) may be much larger than dye nanoparticles etc.
There are other physical explanations for scattering that apply as the solute concentration increases that don't depend on nanoparticles but the specific quantum electronic nature of the excited chormophores also deflecting the incident photons as well, but the end result boiles down to:
You have a given amount of photons move towards the detector through the sample. Some get absorbed, while others fly off in all directions except that of the detector, and then the rest make it to the detector. The detector registers that a fraction of the light you would have expected to reach the detector actually reaches it.
So you are looking at in a semi-simplified way of:
(Number of photons reaching detector) = (number of photons from light source) - (number of photons absorbed) - (number of photons sent off in directions other than to the detector)
At low concentrations, the photons sent in other directions is negligable, they travel in a line and are aborbed or pass straight through. At higher concentrations, some absorb while other incident photons are bounced off and do not pass straight through.
This effect is VERY obvious when dealing with fluorescence systems and using detectors that are at 90 degrees to the incident wavelengths if you observe the same wavelength- you can obseve the incident wavelength on the detector get stronger as the solute concentration increases and scatters it.