According to my course of organic chemistry, para-nitro-aminobenzene has to break his aromaticity to delocalize the electrons of the amino-group in the nitro-group. I don't really see this, when I draw the resonance structures.

According to my course of organic chemistry, para-nitro-aminobenzene has to break his aromaticity to delocalize the electrons of the amino-group in the nitro-group. I don't really see this, when I draw the resonance structures.

Your teacher is correct, some of the resonance structures in your figure are not aromatic. Still though, as resonance structures they contribute to the overall description of the molecule, just less than the structures that are aromatic. The resonance structures at the right and left end of your figure are aromatic. The fourth resonance structure (the one in the middle) is referred to as being a "quinone" rather than an aromatic.
o- and p-benzoquinone are examples of quinones; they are not aromatic compounds (ref, note the sentence "Quinones are conjugated but not aromatic").

Likewise, their carbon analogues, o- and p-xylylene are also non-aromatic quinoid-like compounds.
For a compound to be aromatic it must be
It is this last point that serves to differentiate quinones and quinone-like molecules from aromatic compounds.
Finally, aromatic compounds need not be planar, deviations in excess of 15° from planarity can be tolerated and the molecule can remain aromatic (see, for example, [6]-paracyclophane)

Aromaticity is not a very well defined concept (there are no strict rules) and I also believe that it is hard to tell apart from overall resonance stabilisation. The IUPAC goldbook states for aromatic:
aromatic
- In the traditional sense, 'having a chemistry typified by benzene'.
- A cyclically conjugated molecular entity with a stability (due to delocalization ) significantly greater than that of a hypothetical localized structure (e.g. Kekulé structure ) is said to possess aromatic character. If the structure is of higher energy (less stable) than such a hypothetical classical structure, the molecular entity is 'antiaromatic'. The most widely used method for determining aromaticity is the observation of diatropicity in the 1H NMR spectrum.
See also: Hückel (4n + 2) rule, Möbius aromaticity- The terms aromatic and antiaromatic have been extended to describe the stabilization or destabilization of transition states of pericyclic reactions The hypothetical reference structure is here less clearly defined, and use of the term is based on application of the Hückel (4n + 2) rule and on consideration of the topology of orbital overlap in the transition state. Reactions of molecules in the ground state involving antiaromatic transition states proceed, if at all, much less easily than those involving aromatic transition states.
Hückel's set of rules are often used as nice guidelines, but they are not the definition of aromaticity. In fact they are very, very rigid and strict and most of the compounds you'd usually consider being aromatic in this context, do not comply with these rules. The IUPAC goldbook defines:
Hückel (4n + 2) rule
Monocyclic planar (or almost planar) systems of trigonally (or sometimes digonally) hybridized atoms that contain (4n + 2) π-electrons (where n is a non-negative integer) will exhibit aromatic character. The rule is generally limited to n = 0–5. This rule is derived from the Hückel MO calculation on planar monocyclic conjugated hydrocarbons (CH)m where m is an integer equal to or greater than 3 according to which (4n + 2) π-electrons are contained in a closed-shell system.
In this framework only the first and the last structure obey Hückel's rule. The proton and carbon NMR clearly proof that p-nitroanniline is an aromatic compound, the spectrum is very close to the data of benzene.
Resonance structures are just a crutch to explain a very complicated and complex electronic structure in simple and understandable terms, i.e. Lewis structures. In highly delocalised systems a superposition of all resonance structures has to be considered to paint a somewhat conclusive picture of the bonding situation. There are contributions of different structures and not all of them may be equal in the overall description, however, they do not change the fact, that the experimental property is observed. This is again a case, where you can see the limitations of the resonance concept.
All the resonating structures follow Huckel's Rule and so they are not losing their aromaticity.
A classic example of an aromatic cabanion is cyclopentadiene ion.
The negative charge or the lone pair is in resonance and is in an unhybridised orbital. Hence it gives $sp^2$ and not $sp^3$. So its planar.