Why Alexanders empire not last after his death?

Alexander had no clear heir or successor. He had a handicapped brother and an unborn child to his Persian wife Roxane. It was arranged that when the child was born, the brother and child would jointly take on the rulership. However it didn't happen. Alexander's generals had been given provinces to govern, and these now took control and entered into war against each other. After the first war, the settlement was:

Antipater - European Greece - and regent of the Empire, with under his control king Arrhideus and the boy-king Alexander IV in Macedon.

Antigonus - Phrygia, Lycia, and Pamphylia and Lycaonia.

Ptolemy - Egypt

Lysimachus - Thrace

Seleucus - Babylonia

Peithon - Media

Antigenes - Susiana

After several more wars of succession and the murders of the two kings, the succession settled to:

Cassander - European Greece

Ptolemy - Egypt

Antigonis - Asia Minor

Seleucis - Syria and Mesopotamia.

The governors took the title of kings, and ruled their separate kingdoms (known as the Hellenistic kingdoms) and continued sporadically fighting each other. These kingdoms were progressively absorbed into the Roman Empire in the 2nd and 1st Centuries BCE.