If that is true, then you can NEVER know you are of the elect, as NOTHING you do, even say the sinner's prayer, is enough to know that God has you as one of the elect. Nothing you do can guarantee that you are of the elect. And if a person falls away, as you mention, then that person never had salvation to begin with???
"For if we sin wilfully after we have received the knowledge of the truth, there remains no more sacrifice for sins, but a certain fearful hope of judgment and fiery indignation, which shall devour the adversaries. (Heb 10:26-27)
Paul disagrees with that idea. When we are baptised, we are saved (healed). But we are told to persevere - that our status with Christ and in Him is not permanent - there is the potential of falling away, of losing His sacrifice for sins applied to us. Since we cannot know the future, we cannot know we are of the elect. Our actions today do not necessarily mean we will continue in them in five years.
God works salvation within us, first during our Baptism. THIS is effective assuredly. But this salvation doesn't imply that we will continue to run the race and not be disqualified later on.
Regards
This isn't a message of "perseverance" to Christians. This is a message to the Hebrews that if they reject the truth of the message of Christ to go back to their legalistic laws, there remains no longer a sacrifice for sin. The Law was swept away with Christ.