Generally speaking, yes.  Fired officers shouldn't be hired, however, there should be some leeway so that the individual could be evaluated to ensure suitability.  I know of a few law enforcement officers who were fired for failing to qualify with their firearm.  With remedial training, they all were hired as armed guards, and eventually were hired on as law enforcement officers.

Being fired for dishonesty, committing crimes, etc. should be a no brainer, and these folks shouldn't be allowed to be hired as armed personnel.  However, individuals fired for administrative matters (non-criminal) like qualification, weight, health issues, etc (mainly stuff that can be corrected), should be considered as quality personnel can be hard to come by.