Nero's downfall, in my opinion, came about due to his neglect of the Power groups in Rome, and also his inability to maintain the proper characteristics of the Imperator.
The Power Groups were: The army, the Praetorian Guard, the masses and the Senate.
He decided not to pay the army (which started revolts) and he just stopped proper campaigning, ignored the Senate completely (who became disgruntled and began assasination plans), witheld grain from the public just to see their reactions (and did many other completely atrocious things such as started riots on purpose, burnt down Rome, embarked on serious persecution etc...) and only really kept somewhat in connection with the Praetorian Guard.
Characteristics of the Princeps (Emperor): Stoic (he went against this by deciding to be an actor), dutiful (he ignored all his typical duties of payment, took money from whomever he wanted, engaged in unlawful behaviour etc), maintainer of peace (he caused uproar on purpose) and prosperity (he over spent, then called on the law of maiestas to take away other peoples property to keep the treasury going).
As he failed in most of the areas that an Imperator shoul excel at, he was on a path to downfall through the dissatisfaction of his own people.