I have quickly looked at Arminian doctrine to show you truth behind their thinking. For the question of eternal salvation versus salvation lost has been of a topic through many versions of churches. And also to show how both are correct. The failure that many come to learn is that of the Holy Attitude. For the Holy Attitude is eternally available to all that enter into the peace, and also one can reject this attitude being in need once again of atonement not that another atonement is needed. Only a return to the attitude and the usage of the teachings.
Some bible verses for you to consider so that you may see how just God really is.
Jesus gave us "The Parable of the Wedding Banquet" in this passage we see how we all where invited to come to the banquet of love, peace, and joy.
Matthew 22:10 NKJV
So those servants went out into the highways and gathered together all whom they found, both bad and good. And the wedding hall was filled with guests.
So understand that the servant is Jesus the Son, calling all to come. So notice next that in this next scene the man without the wedding garment was already present in the kingdom.
Matthew 22:11-14 NKJV
“But when the king came in to see the guests, he saw a man there who did not have on a wedding garment. So he said to him, ‘Friend, how did you come in here without a wedding garment?’ And he was speechless. Then the king said to the servants, ‘Bind him hand and foot, take him away, and cast him into outer darkness; there will be weeping and gnashing of teeth.’ “For many are called, but few are chosen.”
So the man was present in the kingdom of God, and then afterwards was tossed out into the darkness.
Notice how many are invited, but notice most of all that it is the "sons of the kingdom" that are cast out.
Matthew 8:11-12 NKJV
And I say to you that many will come from east and west, and sit down with Abraham, Isaac, and Jacob in the kingdom of heaven. But the sons of the kingdom will be cast out into outer darkness. There will be weeping and gnashing of teeth.”
So you see, many branches of Christianity focus how your invitation to the kingdom is secure, and how you are guaranteed to get their by faith in his name. What is failed to be seen, is that once you are their it is by your clothing that you will stay or be thrown outside.
Take notice of the word abide. Defined as "Act in accordance with."
John 15:6 NKJV
If anyone does not abide in Me, he is cast out as a branch and is withered; and they gather them and throw them into the fire, and they are burned.
You will say then, “Branches were broken off that I might be grafted in.” Well said. Because of unbelief they were broken off, and you stand by faith. Do not be haughty, but fear. For if God did not spare the natural branches, He may not spare you either. Therefore consider the goodness and severity of God: on those who fell, severity; but toward you, goodness, if you continue in His goodness. Otherwise you also will be cut off. And they also, if they do not continue in unbelief, will be grafted in, for God is able to graft them in again. For if you were cut out of the olive tree which is wild by nature, and were grafted contrary to nature into a cultivated olive tree, how much more will these, who are natural branches, be grafted into their own olive tree?
So obtain the peace by faith and forgiveness, and remain as well. Notice they are considered clean before he died on the cross. And to bear fruit.
John 15:2-3 NKJV
Every branch in Me that does not bear fruit He takes away; and every branch that bears fruit He prunes, that it may bear more fruit. You are already clean because of the word which I have spoken to you.
John 15:5 NKJV
“I am the vine, you are the branches. He who abides in Me, and I in him, bears much fruit; for without Me you can do nothing.
John 15:16 NKJV
You did not choose Me, but I chose you and appointed you that you should go and bear fruit, and that your fruit should remain, that whatever you ask the Father in My name He may give you.