Why can't Iron fusion occur in stars?

The Sun obviously produces far more energy per second than is required to fuse an iron nucleus with some other nucleus. The problem is concentrating all that energy on the iron nucleus. It's not enough to know that it takes the energy from $n$ hydrogen fusions to fuse one iron nucleus, it's getting the energetic products from those $n$ hydrogen fusion events to all collide with the iron nucleus at the same time. Under normal conditions the probability of this is negligible.

However, under extreme conditions it can occur. For example in supernovae the pressures and temperatures are so high that iron and heavier nuclei undergo fusion reactions to produce the elements heavier than iron.

Iron fusion can take place in stars - what you need is lots of iron and very high temperatures to overcome the ever-increasing Coulomb repulsion between alpha particles and heavier nuclei. These conditions exist in the cores of massive stars near the ends of their lives.

For example alpha particles can fuse with an iron-56 nucleus to produce nickel-60 and then zinc-64; these reactions are almost energetically neutral because the binding energy per nucleon curve is almost flat over this atomic mass range. The problem is that there are competing decay and fission processes (particularly photodisintegration at high temperatures) that act to break up nuclei at these temperatures which disfavour the significant production of heavier nuclei in any kind of equilibrium.

Heavier elements can be produced by neutron capture. This can be an exothermic process, but requires less energetic conditions since the neutrons are neutral and it can occur even near the centres of intermediate mass stars (see Origin of elements heavier than Iron (Fe) ). Heavier nuclei such as Sr, Ba and even Pb can be produced by a chain of slow neutron captures followed by rapid decay events, which are then stable, and the interior conditions at the centres of intermediate mass AGB stars are not hot enough to cause photodisintegration. Neutron capture can also occur more rapidly during a supernova explosion - a highly "non-equilibrium event" where a tiny fraction of the supernova energy goes into endothermically producing the heavier elements and all of those beyond lead.

As you correctly stated in normal situation the star cannot sustain the process. This doesn't mean that there are no such reactions going on in the core. The difference is that during the pre-supernova phase of the star the production of iron is negligible compared to the star. When it goes supernova, it produces a comparable amount of iron.