Convicted four times, but with conviction overturned on appeal (including one time to the Supreme Court), plus two mistrials. The new DA declined to seek a seventh trial.
Ah, that makes more sense. It isn't double-jeopardy when a conviction is remanded for re-trial (although why it's not is unclear to me in a common-sense sense).
You usually cannot appeal simply on the basis that you believe the jury made the wrong decision, i.e. on the basis of an error of fact.
There has to be an error of law (e.g. the judge have a wrong jury instruction, or evidence was inappropriately allowed/excluded, or the trial was allowed to continue when a mistrial should have been declared) or other constitutional basis, like ineffective counsel.
In some cases, appeal courts will decide that there could be no basis for conviction once the flaw is corrected (in which case a conviction can be reversed), but oftentimes the appropriate outcome is to remand the case back to the lower court for retrial.
Was it five or six hung juries?