The "republican" idea is dead once the republic becomes too big to have an easy communication with your colonies.
Communication was an issue, especially looking to the roman system, where a senate as a collective is supposed to rule the state. But that does not mean, that other republican government systems would not have been able to deal with the issue of communication and distance way better. The trick is, to draft a republican system which is scalable
and acceptable for the romans. Perhaps a mission impossible.
It is just hard to draft a POD, where roman aristocracy would accept an alternate republican system, e.g. one with more buerocracy and therefore more classes involved into government, perhaps more local control and finally more division of powers, instead of trusting in annuity, collegiality and the coherence of the senatorial class alone.
I have just read "Werner Dalheim, Gewalt und Herrschaft - Das provinziale Herrschaftssystem der römischen Republik". He shows clearly the helplessness of the roman senate after conquering the first 2 provinces Sicilia and Sardinia. For about 4 years Sicilia was more or less ungoverned, until the senate invented 238 BC the system of proconsulship, with the annexation of Sardinia. Perhaps the first nail into the republican coffin. If not Romulus and Remus, which stands for the roman mindset in general, was the first nail, and Rome was doomed to fail from the very beginning.
The romans had alternatives 241/238 BC, as Dalheim points out, e.g. the italian system of socii, client kingdoms, and others. In the next two centuries the romans kept on tinkering with different government systems, starting shortly later with Cisalpina and Illyricum, which was organized fully differently than Sicilia and Sardinia at the beginning (no proconsul). Spain was a big mess, too. And the show goes on and becomes even more weird in the East with Greece and Asia.
So I personally agree, that the roman republic was almost dead in the first century BC. One important reason was their fully inappropriate system of province-government, which finally stroke back to Rome itself. And the Rubicon is pretty much too late, in order to start a POD which rescues whatever kind of republic. But, as mentioned above, some very prestigious historians liked to disagree lately.