One became a senator in Rome by fulfilling one of the higher offices in the Roman Republic. One could be elected to the lowest of these high offices from 30 years of age (others had higher age requirements). Ten years of military service was required before one could serve in one of these offices.

Additionally, there were property requirements and ethical standards for (would-be) senators. These requirements were checked by censors (arguable the most respected office one could attain) nominally every five years, though there have been periods of (many) decades without censors.

Censors could kick people out of the senate if they no longer met the requirements or standards. The senate could also throw people out of the senate by prosecuting them for misbehaviour. This happened very rarely though. I have told about a few examples here.

So once one had become a senator, it would in most cases have been for life.