Janak does not predict neiter EA and IE. In Kohn-Sham method, the derivative of the ground-state energy of noninteracting electrons with respect to the orbital occupations is equal to the orbital energy. This result is independent of the form of approximation to E_xc. Integrating the orbital energy between N and N+1, gives negative of the electron affinity. (similar is for N-1 and N). In exact theory, the energy of the frontier orbital is const. and equal to the chemical potential. In approximated DFT, only the energy of orbital with fraction around ½ is a good ionization energy (or electron affinity). See Parr&Yang book eqs.7.612.-7.615

There may be some numerical studies of the question raised here, which I do not recollect at this very moment. However, the following two observations suffice to answer this question. (1) The fundamental gap Ε_g is underestimated in the framework of the ground-state DFT, by a well-known discontinuity in the exchange-correlation potential, which is missed out by this potential being deduced on the basis of number-conserving variations δn(r) of the ground-state number density n(r).* (2) E_g is equal to the first ionization potential minus the electron affinity. Now, if one of the two quantities, whether the first ionization potential or the electron affinity, is predicted relatively accurately by the Janak theorem, from (1) and (2) it follows that the other cannot be predicted accurately by this theorem.

* For some relevant discussions, see:

http://journals.aps.org/prb/abstract/10.1103/PhysRevB.32.3883

Recall that the Euler-Lagrange equation δE_v[n]/δn(r) = μ follows from the ground state being a stationary state *and* the integral of δn(r) being vanishing.

Janak does not predict neiter EA and IE. In Kohn-Sham method, the derivative of the ground-state energy of noninteracting electrons with respect to the orbital occupations is equal to the orbital energy. This result is independent of the form of approximation to E_xc. Integrating the orbital energy between N and N+1, gives negative of the electron affinity. (similar is for N-1 and N). In exact theory, the energy of the frontier orbital is const. and equal to the chemical potential. In approximated DFT, only the energy of orbital with fraction around ½ is a good ionization energy (or electron affinity). See Parr&Yang book eqs.7.612.-7.615