I'm in the minority, I think that the empire could have lasted in a respectable form for at least a century after Alexander's death. It all depends on who succeeds him and how smoothly it goes. The institution of leadership had to be tested and in OTL it failed but if you give Alexander a long enough life post-India then he can do some much needed tweaking of the Empire, allow the bloodmixing initiatives to bear fruit and maybe quietly retire some generals and keep the armies closer to Ctesiphon Babylon so everyone doesn't get a chance to landgrab at every succession.
Consider me in the minority as well.
The hardest thing with this scenario is actually
Alexander living into his 50-s.
The rest is not that difficult to guess.
But let's say that during his Arabian campaign Alexander in his usual reckless suicidal manner got involved in the hand-to-hand combat. He fell from his horse, broke his both legs, had his right arm cut off, had a spinal injury and a handful of minor wounds. But he did not die, continued living able to move only in a stretcher/palanquin.
And he didn't kill himself quickly by alcohol as he had something like a religious revelation or something like that, becoming a true philosopher out of a suicidal fighter.
My point here is that Alexander living longer equals Alexander keeping his empire in the borders we know in OTL.
Which is understandable as he personally cannot lead his armies and at the same time he is envious to his generals - he cannot let anyone become as famous as himself. He was paranoid in OTL, he would be double paranoid in this ATL.
His generals would be entrusted with armies only when it's absolutely necessary - in case of invasions and punitive expeditions.
- What will the Empire look like?
- I guess, something like the Seleucid Empire of OTL.
But, there will be some differences:
1) it will be bigger of course. The Achaemenid Empire + Macedon/Greece. Most of the time, I guess with sporadic breaking away of some rebellious satrapies like Bactria or Egypt or some others.
2) The Hellenization will be different from OTL. The scale will be bigger, as from the very beginning the process will start from both ends - Barbarization of the Hellens/Macedonians and Hellenization of the "Barbarians". And it will be deeper, a little bit closer to amalgamation, like Alexander the Great desired.
3) But there won't be a "true amalgamation" of the conquerors and the conquered. This did not happen in OTL, that won't happen in ATL.
Because in this ATL there will be a great pool of the Macedonians/Greeks for the Empire,
much bigger than in OTL Seleucid Empire or Ptolemaic Egypt. So there's even less incentive to rely on the locals in this ATL.
4) Military speaking the Empire will be much stronger than OTL Seleucid/Ptolemaic Empires. In OTL the power base of the Hellenistic kingdoms was dramatically small - the 'ethnic' Macedonians/Hellenes and the Hellenized local elites - about 3-5% of the total population at best.
Here in this ATL these Hellenes/Macedonians/Hellenized might be up to 10-20% of the total population of the Empire, which is a
huge difference from OTL.