Arcadius and onward, per the rules of my last poll. Latin Emperors, Muscovites, and any other non-Greco-Roman pretenders are not allowed. 
I feel this is a bit harsh. Heraclius may have lost Egypt and Syria to the Persians, but this loss was only a temporary setback. Heraclius spent the time during which these losses happened rather wisely and managed to prepare the Empire for a counter attack, which after a few delays performed brilliantly. Heraclius wasn't the catalyst for the war, Phocas was and I don't think Phocas, or anyone else for that matter would have done even half as good as Heraclius when it came to repelling the Persians.Heraclius, on the other hand, I feel is overrated. For all that Phocas gets maligned in the sources, the big losses in the war against Persia (viz. Palestine, Egypt, and Asia Minor) all came during Heraclius' reign. Sure he managed to pull the Empire back from the brink of destruction, but he was the one who'd brought it to the brink of destruction in the first place.
While there are no known surviving eyewitnesses to his death, Michael Critobulus (writing in Mehmed's service) later describes that upon finding the city was lost and yet he survived, Constantine tore off his imperial ornaments so as to let nothing distinguish him from any other soldier... and led his remaining soldiers into a last charge. The fact that no positively identified body was ever found just adds to the mythology.
I don't know, I've heard that he could also have been tearing off his vestments and armor in order to escape as a civilian.
I feel this is a bit harsh. Heraclius may have lost Egypt and Syria to the Persians, but this loss was only a temporary setback. Heraclius spent the time during which these losses happened rather wisely and managed to prepare the Empire for a counter attack, which after a few delays performed brilliantly. Heraclius wasn't the catalyst for the war, Phocas was and I don't think Phocas, or anyone else for that matter would have done even half as good as Heraclius when it came to repelling the Persians.
The plague was not his fault-but the response was: seriously, what was the point of clinging on to Spain and the Ravenna-Rome corridor after that?
The Ravenna-Rome corridor is the fault of Justin II. The Lombards didn't move into Italy until after Justinian's death.
Yeah I mean sure, that's a valid point. He also didn't spend the 9 years waiting, Heraclius did make some attempts to stop the Persians from invading Syria and failed. Although I can't put too much blame on the short loss of Egypt as many Copts simply let the Persians in due to dissatisfaction with Constantinople's religious policies. So he clearly made some mistakes and bad choices, like every Emperor, however his execution and importance are what matters, and by those factors Heraclius did the best anyone could in such a terrible situation overall. Infact I'd almost go so far as to say that if it was anyone else but Heraclius, the Persians would have won that war and the Romans would become a Sassanid puppet/tributary before being destroyed or weakened by the Arabs.Sure he needed to prepare for a counter-attack, but nine years seems a bit long, especially when the enemy are invading your most productive provinces and thereby making your counter-attack more difficult. Waiting so long was a massive gamble, a gamble which paid off, but still a gamble. Had Heraclius done everything up to 622 the same and ended up failing in his counter-attack, I've no doubt people would be blaming his sitting back and doing nothing whilst the Persians occupied the eastern provinces.