I think with the right choices the Republic could have been saved. What it needed was bigger government, more government benefits, more taxes, and less political privilege for its oligarchy.
This completely contradicts the Taylor Caldwell idea that the Republic fell because they were like Great Society liberals, so let me explain.
Republican Rome had nothing like a police force or fire department, although many Greek cities had had them for centuries. It finally got both under Augustus: urban cohorts and the vigiles, a combination of night watch and firemen. Their absence allowed the political gang violence of people like to Clodius and Milo to be highly effective in the late Republic, and allowed people rich enough to own their own fire department, like Crassus, to show up at your burning house and demand an extortionate fee to put it out.
The late Republic made little use of civil servants to collect taxes, instead selling the right to collect particular taxes for a flat fee. The tax farmers had strong incentives to collect excessive taxes, and there were frequent complaints that they did so. It was a bad deal for the state and the average citizen, but it allowed those wealthy enough to advance the payment an opportunity to become even richer.
It also had no regular policy for rewarding soldiers who had completed their term of service with land to support themselves after their service. Such grants were made, but only when successful and powerful generals pressured the Senate to do so. This, of course, tended to align soldiers loyalties with the generals rather than the state.
A sales tax on slaves would have raised considerable revenue, and one was instituted under Augustus, but the Republic had none. Such a tax could have funded public services like police and fire fighters, and civil servants to collect taxes. Also, anything that made slaves more expensive would have mitigate the negative impact of the slave worked latifundia on free farmers of small holdings.
The Roman Republic made many unwise choices, in large part because the Senatorial oligarchy had an inordinate share of power under the Roman constitution, and they tended to make choices that favored their own self interest, rather than that of the Republic as a whole. But the constitution of the Roman Republic was not immutable: it had at times been amended to force the privileged to cede power to the less powerful.
It is one of the great tragedies of the late Republic that the reformers were too bold and the conservatives too obdurate. It ended in tears, and imperial rule.