Is it possible that there are more than 6 quark flavors/more than 3 generations? I thought that things like the top quark don't exist in nature because they're super unstable and we can only observe them after high-energy collisions (e.g. LHC)
Is it possible to make even more massive quarks?
Or is there a reason the limit is six?
 A: To our knowledge, there are three weak generations of particles, so there are three copies of the neutrino/electron lepton pairs, and three copies of the quarks.  
It's possible that there is a fourth generation, but it is also likely that the evidence for this fourth generation would appear as a new neutrino before we discovered a seventh quark, since the neutrinos are less massive than the quarks, and we don't have to worry about sorting through the messiness of strong particle decay in order to find them.
A: I know it's not mainstream physics, but here I go again (it's always good to know non-standard approaches). According to this beautiful theory, quarks and leptons are not fundamental particles, and according to this model, the higher generations are excitations of the first generation. So maybe at very high energies, the constituent particles (of the quarks and leptons) can be excited to a fourth generation, while it's also plausible that at such an energy the excitation is such that no higher generations are formed but high-energy standard particles. 
That there are no more than three generations was predicted in this experiment in connection with the decay of the $Z$-particle (one of the three massive particles that convey the weak force). In the model I referred to also these particles are composite though, so I think it's still an open question. Or maybe it really shows there are (in the light of this model) no more than three generations, and an eventual fourth one can't be excited at very high energies.  
