Eventually, parts will break off. Nothing goes right for any one empire indefinitely, so a time of decline and unrest and splintering will eventually come. But that time is not likely to be in the immediate future. Alexander hit them at a bad time, when they were still recovering from a succession struggle / civil war. The strain of that war had forced them to tax local governors to an extent that had caused resentment. (And not just in money, but in resources and in fighting men levied.) Alexander exploited that, too, swaying Satraps to his side by promising a lighter touch, less taxation and more self-government. But without his campaign, the Akhaimenids have all the time they need to get their house in order. The worst is behind them.
The Macedonians have a succession struggle ahead of them now, and there's a good chance the Greek poleis will take the opportunity to revolt. How eager the Persians will be to fund the city-states in this endeavour! How ready they will be to turn all Greeks against all other Greeks, and watch them kill each other. Squabbling little upstarts, their spears turned on each other. Things are looking good for the Akhaimenid Empire.