This is an interesting one; I've covered it in my 2011 book 'If Rome Had Survived' (Pen and Sword HB) as one of the main 'what if' arguments of how the Eastern Empire could or should have been able to fight off the Arabs in the 630s if there had bene no, or a more swiftly concluded, Sassanian war in the 620s. Given the concentration of Roman troops in Mesopotamia against the Sassanians with or without a major war there plus the shortage of men and money since the huge losses of the Justinianic plague in 542, it is pretty clear that any Emperor would have neglected the defence of the open desert borders in Syria and Jordan and been taken by surprise by the strength and unity of Arab attacks. Also the apparent factor of underpaid or ignored Roman mercenary Arab tribes , who also coveted fertile Syrian land for their flocks, defecting to the Caliphate once it appears to have an army capable of winning is probable, and this would give the Arabs local scouting help and cut off the Empire's supply of cavalry irregulars to harass Arab armies - unless the OTl collapse by c. 630 of the Empire's main Arab ally state in E Jordan/ Golan Heights/ SE Syria, the Ghassanid confederation, does not happen so Rome has their substantial cavalry force to help it .
If Rome had had a stronger presence in the area, due to no Persian war or paying its irregulars better or no Ghassanid collapse, you get only sporadic Arab infiltration and raids and probably no open major battle, at least until Rome is exhausted by the constant warfare and can be taken on in the field - but this would be enough to wreck agriculture in Syria and Palestine, cut off isolated towns, and lead to gradual collapse in the manner of Italy when the Lombards invaded after 568. Thus the Empire's position gradually collapses and it can at best hold onto major towns and the coast cities as it did in S Italy in the 570s to 600s - with swifter collapse if the Arabs take out Persia instead in the late 630s and acquire its manpower and its military siege hardware.
If an Emperor is able or willing to bring in a big army and tackle the Arabs, he can take back lost towns temporarily and achieve a false sense of victory ( as Constans II did in Italy in the 660s) but either it all collapses once he goes home or he gets caught chasing elusive nomads around bleak and hostile countryside , running short of provisions and his men getting tired and fed up. That way lies a Manzikert-style disaster at the hands of the Arab archers and cavalry skirmishers. The loss of most of the 'Levant' (ie Syria/ Palestine/ Lebanon/ the upper Euphrates) minus the coast and a few big cities is probable within a few decades - sooner if an earthquake demolishes city walls at the wrong moment.
The fall of Maurice is largely due to his short-term pushing for the Balkan army to winter N of the Danube while tackling the other main nomad raider threat of this era, the Avars who are based in what is now Romania and SW Ukraine; the plan was to wreck the Avars' homeland's settlements and food supplies and force them into a truce which their leader (the 'Khagan') would be sure to keep for at least a few years. The demoralised and already faction-ridden army , which had a history of throwing out disliked generals and defying imperial orders so its revolt was not out of the blue, mutinied and marched on the capital and as it arrived an insurrection broke out there too - Maurice was disliked, eg for high taxes and parsimonious spending, there too . M and his six sons (all, or all but one, under-age so not viable to replace him in a coup) were killed and the army too over, installing its own , low-born ex-ranker spokesman Phocas as emperor. He was defied by assorted provinces and could not rely on the elite in the capital despite allying himself to some of the nobles , and civil war followed - though it is arguable if he would have turned into a 'tyrant' and oppressor in any case or if this was a panicked reaction to the strength of opposition. A non-elite and non-Constantinopolitan/ army high command Emperor was something new and unacceptable to many; so a more 'respectable', officer choice as the new ruler by the mutineers might not have sparked off a civil war and purges. Ditto if there had not been a pretender from Maurice's family, allegedly his eldest son Theodosius (late teens?) , available to flee to Persia and ask the Sassanian 'Great King' Khusrau/ Chosroes II for help - in fact he was probably a fake. Khusrau was M's client, who M had put back on his throne in 590 after a Persian coup deposed him, so he had links to M's family and was keen to help them, and to take as much of the Empire as he could in return - and if T was a fake he may have deliberately set him up as an excuse to attack the 'usurper' Phocas. Given that he had been put back on his throne in place of a usurper military noble Great King by the national enemy and could be seen as a 'Roman puppet', attacking the Empire also shored up his own legitimacy.
A long war followed , and exhausted the Empire to add to the 602-10 civil war (which in the end Heraclius, son of the governor of Carthage/ Tunisia, posing as Maurice's avenger, won) and more famine and plagues. By the time the Empire won in 629, much of Anatolia had been ravaged and the Persians had occupied Syria/Palestine/ Egypt for some years; the Empire was in no fit state to fight anyone, let alone mobile and determined Arab desert warriors who were an unusual foe compared to the usual Roman 'heavy infantry and cavalry' opponent Persia. So if M - an abrasive character, but a general with a good reputation from the Persian front when chosen as heir in 582 - avoids pushing his Balkan army too far (not for the first time, a she had previously ordered them to winter in enemy territory and had also annoyed them by refusing to spend scarce money on ransoming prisoners) and is not overthrown in 602 or he is replaced by someone more 'elite', we probably don't get a long civil war. Persia does not attack then and as an ally of M probably stays quiet as long as he is alive (he was aged c. 60 in 602) , though a war may occur later with his weaker son or with a usurper. That way, the Arab incursions develop on a slower 'arc', as outlined above.
But to make the Empire stronger in the long term and able to hold the Arabs back better, and to tackle the Avars in the 570s - 600s as well even if Persia is quiet, you need a different emperor in the period -or one who does not stay in the capital but goes on campaign himself and so is closer to and trusted by the troops. No emperor had done this since 395 - even Justinian did not go to the frontiers. Result: an elite out of touch with the realities and at more risk, or one seeking bravely but stubbornly to shore up a crumbling state with far too small resources? To avoid that overall problem, no Justinianic plague and/or no distractions in Europe (eg no Lombard invasions of Italy or the Avars not choosing to raid the Balkan s but moving West into central Europe) is the best option. To get a better emperor - or at any rate a less unpopular one - by 600, possibly avoid the succession of Justinian by his impulsive, unstable nephew Justin II (the man who first annoyed the Avars by refusing to pay them off, though they would probably have attacked at some date anyway) and have his other nephew, another but more capable and better-liked Justin, succeed him in 565 and his sons then succeed him; J II's being chosen as heir, if he was indeed chosen by his uncle not installed in a plot by courtiers when Justinian died suddenly, was due to manipulation by his mother, Justinian's sister Vigilantia, and his wife Sophia, niece of Justinian's late wife Theodora. Possibly a more stable Empire in 570 - 630 follows.
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