Existence of a perfect blackbody Why is a perfect blackbody not possible? On an electronic level, what is the reason for the non-existence of an ideal blackbody?
 A: 
On an electronic (sic)  level, what is the reason for the non-existence of an ideal blackbody?

This is based on Black Body Wikipedia

A widely used model of a black surface is a small hole in a cavity with walls that are opaque to radiation. Radiation incident on the hole will pass into the cavity, and is very unlikely to be re-emitted if the cavity is large. The hole is not quite a perfect black surface — in particular, if the wavelength of the incident radiation is longer than the diameter of the hole, part will be reflected. Similarly, even in perfect thermal equilibrium, the radiation inside a finite-sized cavity will not have an ideal Planck spectrum for wavelengths comparable to or larger than the size of the cavity.

In my comment above, I mentioned the Cosmic Microwave Background Radiation spectrum and I would like to explain why I used that particular example:

Why is a perfect blackbody not possible:

In nature, it is  possible to observe an almost perfect blackbody spectrum. In the picture below the extract, you see the  error bars as an indication of just how close the CMB radiation is to as what we predict by  Plancks's Law.

The big bang theory is based upon the cosmological principle, which states that on large scales the Universe is homogeneous and isotropic. According to theory, the Universe approximately a second after its formation was a near-ideal black body in thermal equilibrium at a temperature above 1010 K. The temperature decreased as the Universe expanded and the matter and radiation in it cooled. The cosmic microwave background radiation observed today is "the most perfect black body ever measured in nature". It has a nearly ideal Planck spectrum at a temperature of about 2.7 K. [My emphasis].  It departs from the perfect isotropy of true black-body radiation by an observed anisotropy that varies with angle on the sky only to about one part in 100,000.


Image Source: Big Bang Duke University
A: 
Why is a perfect blackbody not possible?

Have a look at how the black body radiation formula is derived:

From the assumption that the electromagnetic modes in a cavity were quantized in energy with the quantum energy equal to Planck's constant times the frequency, Planck derived a radiation formula

So the basic assumptions are really statistical, not looking at the individual atomic molecular and general electronic levels.

On an electronic level, what is the reason for the non-existence of an ideal blackbody?

Thus, depending on the accuracy of measurements of the spectrum there will be differences to the curve itself even for solids. Specific molecular transitions may become prominent and the planck function will be only approximated.
Look at the spectrum from the sun:


Solar irradiance spectrum above atmosphere and at surface. Extreme UV and X-rays are produced (at left of wavelength range shown) but comprise very small amounts of the Sun's total output power.

You can see that the spectrum coming from the sun is approximately following the black body curve, and here the type of matter on sun plays a role on changing the shape.
For gases it is much worse than for solids, they do not follow the mathematical formula very well with peaks and valleys intervening. Have a look at this analysis where the atmosphere is discussed.

Thus the CMB black body is a very good fit to the black body formula, to an accuracy of 10^-6 because of the quantum statistical nature of the original homogeneity,. 

The cosmic microwave background (CMB) is an almost-uniform background of radio waves that fill the universe.  The CMB is, in effect, the leftover heat of the Big Bang itself - it was released when the universe became cool enough to become transparent to light and other electromagnetic radiation, 100,000 years after its birth.  At this time, the universe was filled with a hot, ionized gas.  

Even there deviations have been found when errors are pushed to the limit, due to the topological shapes , inhomogeneities at the time of the decoupling of photons:

It is believed this smoothness comes about because of inflation, a time of extremely rapid expansion in the first 10^-34 seconds of so of the universe's existence. This rapid expansion smoothed out any lumpiness the universe may have initially had, but quantum mechanical fluctuations introduced new ones - tiny fluctuations of density at all length scales. These tiny fluctuations have grown with time due to gravity (slightly denser regions attract more stuff to become denser yet), eventually providing the seeds for the galaxies and galaxy clusters we see today.

A: A perfect blackbody would be in thermal equilibrium with an isotropic radiation field and absorb all light, at every wavelength, that was incident upon it. The microscopic details are really of no consequence at "the electronic level".
These two restrictions are rarely compatible. An example will help.
The interior of the Sun is very close to a blackbody. A photon generated close to the core has essentially zero chance of making it to the surface. However, even here there is a temperature gradient; photons are not emitted and absorbed at the same temperature and the radiation field is slightly anisotropic and therefore departs from the Planck function. However, the radiation is close to blackbody because the mean free path is small compared with the scale length of the temperature variation.
The approximation becomes much worse as we approach the surface of the Sun. Now the mean free path can exceed the temperature scale length or photons can escape entirely. The radiation field is highly anisotropic. Whether photons escape depends on their wavelength and so both blackbody requirements are invalidated.
In practice it is extremely difficult to arrange to have an object which is "optically thick" at all wavelengths and is isothermal throughout. Wherever there is a "surface" where the radiation can escape then this will tend to cool the object at that point, introduce anisotropies in the radiation field and allow photons to escape without absorption.
An exception is the cosmic microwave background as pointed out in other answers. Why is this such a good blackbody? First, the universe was almost entirely at the same temperature and second, photons could not travel far before being absorbed. The radiation field was and is highly isotropic (to one part in $10^5$) and because we are inside the universe there is no issue of photons having to escape to be observed. In addition, the photons we do "extract" from the radiation field are such a tiny fraction of the total that it cannot disturb the isotropy.
