Maintenance of patrician status required the possession of a certain amount of property, or else a censor (provided there was one elected that year, their elections were extremely irregular) might strike you from the roll. This is the same for all the orders--enrollment in your class for the comitia centuriata was based entirely on property. We should not, however, think of the patricians as the aristocracy, because they're not. At least not after the plebeians gained political rights during the Conflict of the Orders, which occurred extremely early in the Republic. Plebeians were admitted to senatorial magistracies, and thus given entry into the senate, at an extremely early date, and by the 1st Century, B.C. there were at least as many plebeians in the senate as patricians, and probably more (the decreasing number of patricians also contributed to this--the OCD notes that of the 50-some-odd patrician clans we know of in the 5th Century, only about 14 are still known by Caesar's lifetime). The aristocracy was the senatorial class, those individuals who had held the quaestorship or a higher magistracy and were thus admitted at the end of their term into the senate. The patricians traditionally were composed of the original senators, back when it was an advisory body for the kings, but exactly how they were enrolled and what qualified them is very unclear, made no less difficult by the fact that many of the patrician clans were not Roman, but from neighboring Italian peoples. But the senatorial class was hardly exclusive to them. Within the senatorial class was a very small group, the nobiles who could also be thought of as the aristocracy. The nobiles were those descended from a consular ancestor. They were a very small group, particularly since the consuls tended to be constantly elected from their ranks, but they were not all patricians--the tradition of electing a plebeian consul alongside a patrician one each year guaranteed that at least as many plebeians were admitted into the ranks of the nobiles as patricians. We run into a lot of problems when we assume that the aristocracy was composed entirely, or even mostly, of patricians--Crassus, Pompey, Brutus, Cassius, Octavian (before his promotion to patrician status), Cicero, Marius, Antony, etc. were all of plebeian status, but were also of senatorial rank, either as novi homines or by much older family lineage.