Considering the half-lives of the lightest and heaviest Fe-isotopes are:
Fe-45 t1/2 = 1.89 ms
Fe-72 t1/2 > 150 ns
In the case of Fe-72, it's not around long enough to add a neutron.
Mn-44 t1/2 < 105 ns, so Fe-44 is likely to have similarly short half-life, or simply not be stable enough. Absorption of a neutron is not practical given the absence of Mn-43, and the fact that Mn-44 decays by e+ or ε, so Z decreases. An (n,p) reaction is not feasible due to the absence of Co-44, although Co-44, if is existed should decay by e+ or ε to Fe-44, which should also decay by e+ or ε.
One could try a collide the appropriate isotopes of Al (Z=13) with the appropriate isotopes of Si (Z=14) to produce Co-44, e.g. collide Al-22 with Si-22 or Si-23 (or Al-23 with Si-21), depending on spallation of a neutron or not. However, one has to look at the half-lives of the reactant radionuclides Al-22 (t1/2 = 59 ms) and Si-22 (t1/2 = 29 ms) or Si-23 (t1/2 = 42.3 ms). The reactants have relatively short half-lives which makes it rather infeasible to use them.
One could collide, Al-22 with Al-22, and assuming there is no loss of neutrons, one could obtain Fe-44. If there were spallation of n's involved, one might have to try using Al-23, on Al-22. Or one has to try lighter (Z-1, Z-2, . . .) isotopes onto heavier (Z+1, Z+2, . . .) isotopes (where Z=13), e.g. Mg on to Si. But same problem trying to make Co-44; the precursors have short half-lives. Using heavier stable isotopes of Al, Mg, Si, would required spallation of neutrons to obtain Fe-44 or Mn-44.
One also has to look at the literature to see if the radionuclide as actually been experimentally created and detected, or is it simply a theoretical calculation. I seem to remember that the requirement to be included in the chart is that the radionuclide either exists or has been created.
Perhaps Fe-44 exists very briefly in supernova.
I'm not sure why one would do that given that there are no practical applications for extremely short-lived radionuclides.
Furthermore, the metastable (m) states of radionulides are not considered separate isotopes. The are simply the same isotope in an excited state that has a probability of decaying by gamma-emission, without changing atomic number Z, or atomic mass A. So there are 28 identified isotopes of Fe, not 34.