score:6
The main institutions were the Senate and the military. The personal wealth and power of the members of the Senate, and the rivalries that ensued, threatened to tear the state apart.
The creation, and expansion, of a permanent military force, spread across the empire and with each part loyal its own general, who was appointed by the Senate, added a military wing to those senatorial factions.
As the empire grew, so did the status of the senators, who gained most from the profits of war and conquest. This exacerbated rivalries between individuals, who also had more resources available to them. Members of the senatorial class were generally arrogant and unaccountable for their actions. Eventually, this would lead to the First Triumvirate 59-53 BC.
The acquisition of an empire required that Rome maintain a permanent military establishment in its provinces to cope with rebellions. These were often loyal to their commanders, rather than to the Senate in Rome, as in the cases of Marius (consul in 106 BC & 104-100 BC) and Sulla (consul in 88 BC, & dictator from 82-79 BC).
It is interesting to note that during Sulla's two year term as dictator, he was supposed to have had well over a thousand of his political opponents put to death. This resolved the problem of factions within the senate (discussed above), and Sulla was able to retire from office, eventually dying peacefully in his bed.
The legions were increasingly being recruited from the provinces, rather than consisting of men from Rome. Even by the 2nd century BC, many of these provinces were beginning to demand full Roman political status commensurate with their role in maintaining the empire. This would result in the the Social War in 91-88 BC.
At the same time, the expansion of citizenship was also substantial in the late Republic. In 129 BC the Roman census recorded some 294,000 (male) citizens. This number jumped to about half-a-million in the census of 84 BC (following the settlement of the Social War).
By the time of the census conducted by Augustus in 27 BC, that number had reached 5 million!
The senate had debated reforms, but these were too little too late.
Upvote:1
The answer of sempaiscuba is great, but I have found some other institutions that were obsolete:
Magistarial annuality
All republican magistrates (except the censors) held their mandate for a single year. At the creation of the republic, the duties of the consuls (only executive office by then) were rather simple: If war broke out with some adjacent city-state, they had to conscript legions and lead them into battle. One such case could be resolved in mere months.
By the end of the republic roman life, diplomacy and economy grew extremely complicated.
The complex legal, economic-regulatory, civil-engineering, etc. processes magistrates like aediles, praetors and questors had to oversee demanded professionals. Not some young senator seeing the office as a possibility to get popular, but someone willing to spend decades in it. The areas of knowledge needed to run the city were simple too diverse to be learned through a single cursus honorum. It is also noteworthy how emperors split up the former republican lower magistracies, appointing for example special officials for corn supply, aquaducts, street maintenance, etc.
It was similar by the military commands. If some chieftain in Gaul or Hispania, or petty king in Asia agreed to become a client/ally of Rome, he essentially made a deal: He had given up the profit he could have gained by raiding in roman territory, and allowed roman knights to take trade advantage, while in return he got the protection of SPQR and had not fear war with Rome.
For such a deal to be profitable, the chieftain had to be sure the the next governor arriving in the next year would not bring permission with him to increase his wealth by sacking his petty state. (due to some political change in Rome the chieftain knew nothing about) A single emperor -- and his legates and procurators responsible top him -- allowed stability in diplomatic relations.
Direct democracy via assemblies
The Roman Republic had a number of voting assemblies capable of making important decisions (like electing magistrates and tribunes, passing laws and plebistices) that convened in the City, and worked only by personal attendance. This gave an unjust benefit to citizens living in Rome over the ever-increasing citizenry of the colonies. Even if they had obtained citizenry, they could only use the private part (marriage, business, legal protection) of it, but were unable to excercise their political rights and the benefits it brought (ie.: bribes and public banquets)