My apologies for the confusion...
I guess I'm asking when a sequential space fails to be an Fréchet-Urysohn space.
A sequential space is Fréchet if and only if it does not contain a copy of the Arens space. This theorem is proved, and the Arens space is defined, in Dan Ma’s Topology Blog. (Note the links at the end of the article to previous posts on sequential spaces that may also be of interest.) Note that the Arens space is not the Arens-Fort space described in Wikipedia; the latter is a non-sequential subspace of the former.
The standard example for a sequential space that is not Frechet is Arens space. The space is described in a general topology book or in wikipedia.