what were the main factors that played a role in the downfall of the Persian Empire

Answer

Very formally, there was the invasion of Alexander the Great in 334-331 BC, culminating in the fall of Persepolis in 330 BC. But the Persian Empire had been weakened before. The main cause of this was precisely the power of the empire: absolute unification. Besides the imposition of a unified language and a unified religion, the laying of ‘highways’ throughout the empire, the Persians had an absolute monarchy as a form of government. The governors or satraps acted as the king’s ‘eyes and ears’ and were themselves under the constant control of the autocrat – for example, they themselves could not call in the Persian army (including those garrisoned in their province). This concentration of power eventually caused the empire to implode: too few people ruled too large a state.

• Too few people: there were the dynastic vicissitudes of the Achaemenids, which made succession to the throne difficult. Coups (Artaxerxes I, Bogoas) and the murder of relatives (Artaxerxes III) weakened the administrative class of the empire, until Darius III established a central government, after which he was also killed and succeeded by someone from his entourage (Bessus).
• Too big a state: the empire also expanded again and again, with Egypt in particular being a tough nut to crack and absorbing military efforts – the Turkish peninsula was overrun by Greeks led by Alexander’s father, while Darius III had just conquered Egypt recaptured, and was therefore active elsewhere.