Actually, no. The Bible does teach that by enduring you show you are saved. Do you really believe YOU can endure to the end
in your own strength? The only one who will endure to the end is the one with God living within them, and working within them
to bring them to an "expected end".
Eternal life is not something that can be "earned" or "attained" by enduring. It is a gift that CAUSES you to endure---and the very reason
you can and do is because you are saved.
Actually, no. All of the "if - then" clauses in the NT relating endurance, continuing, keeping on, holding on, persevering and such with attaining eternal life go the other way. Here are just a very few of the very many examples:
Joh 8:31 So Jesus was saying to those Jews who had believed Him, "If you continue in My word, then you are truly disciples of Mine;
Joh 15:7 "If you abide in Me, and My words abide in you, ask whatever you wish, and it will be done for you.
1Co 15:2 By this gospel you are saved, if you hold firmly to the word I preached to you. Otherwise, you have believed in vain.
Col 1:22 But now he has reconciled you by Christ's physical body through death to present you holy in his sight, without blemish and free from accusation--
Col 1:23 if you continue in your faith, established and firm, and do not move from the hope held out in the gospel.
In each and every instance, the continuing, the abiding, the holding is the condition upon which the conclusion is based.