The Sassanids besieged Constantinople twice. Heraclius was considering fleeing to Carthage, but was persuaded to stay at Constantinople. If he had fled, morale would likely have collapsed, and an opportunity to take Constantinople might have opened up.
IIRC Heraclius was considering surrendering to Khosrow, ceding most of the Empire to him and becoming a vassal, but a significant victory in Anatolia put that thought to rest. If the Romans had been defeated, perhaps Heraclius would've sued for peace.
The Avars nearly captured Thessalonica, and more importantly, they nearly captured Heraclius at Heraclea while in negotiations, though Heraclius managed to escape back to Constantinople. If this had been successful, this would've immensely helped the Avars, and through them, the Persians.
For a true victory in the war of 602-28, someone needs to capture Constantinople (or force it into a peace agreement, as Shahin's campaign nearly did). As long as an Emperor held Constantinople and had an army, the Roman Empire could resist onslaught. Khosrow also needs to ensure the loyalty of his generals, notably the loyalty of Shahrbaraz, who was likely contemplating revenge against him after Khosrow plotted to remove him from power due to his successes. Khosrow also needs to ensure foreign powers, like the Gokturks (who did quite a lot of damage to the Persians and were a large part of success the Roman counterattack. The Persians had many opportunities to win the war. The Persians had their own administrative, dynastic, and religious issues, not to mention the issues that may arise from how they are going to administer and interact with the new provinces they have conquered... So I think the greater question than winning the war is how they will win the ensuing peace.