Every single politcal system has it's flaws and under the right(or this case wrong) circumstances it can or will fall, as every politcal system will eventually.

The flaws of the late republic would have been it's vast size, and that too much power would be vested in single men. I.e Marius, Sulla, Caesar. There was also tension between the classes with an imbalance of power established from the start, followed by ambitious(and possibly sincere) men attempting to undermine the senate trhough the assemblies and resulting in assainations and murders which would only hope to fuel the fires.

The several civil wars that followed just saw solitary figures with their loyal troops(as mentioned earier) taking on a government that had no stability and that had been wracked by inefficeincy and overstrecth. Eventually a figure whom didn't stand for the ideals of the republic would build a base from which it could never return.

It's not to say the republic was useless. It expnaded Rome from a provincial backwater and a nation with a sphere of influence barely encompassing Central Italy and ended with land from Gaul, Egypt, Syria, Asia Minor, Iberia, Africa, Greece, Macedonia.... and one of the greatest cities of the ancient world. It just wasn't designed to govern the area it conquered or handle the greed and ambition of it's members when the money it dealt with reached the levels it did.