Could you please quote any Catechism of the Catholic Church where it is stated that believers enjoy eternal security?
Also note the following (emphasis mine):1030 All who die in God's grace and friendship, but still imperfectly purified, are indeed assured of their eternal salvation; but after death they undergo purification, so as to achieve the holiness necessary to enter the joy of heaven.
Put together these ideas, and if this life is for you Purgatory, then you can enjoy eternal security.1472 . . . sin has a double consequence. . . . every sin, even venial, entails an unhealthy attachment to creatures, which must be purified either here on earth, or after death in the state called Purgatory. This purification frees one from what is called the "temporal punishment" of sin. . . . A conversion which proceeds from a fervent charity can attain the complete purification of the sinner in such a way that no punishment would remain.