For me, the knowledge that my eternal state is in the hands of Jesus, not my own, is a source of great comfort. The strength of His hands cannot fail: "My sheep hear My voice, and I know them, and they follow Me. I give them eternal life, and they will never perish, and no one will snatch them out of My hand. My Father, who has given them to Me, is greater than all, and no one is able to snatch them out of the Father’s hand" (John 10:27-29). The Father and the Son act together to keep me in their love, not just for the rest of my life, but for all eternity. What peace there is in that knowledge! I can understand why Arminians want to hold this truth, contrary to the rest of their free-will theology.
Paul also has a very tender statement about the doctrine of perseverance: "As for the one who is weak in faith, welcome him, but not to quarrel over opinions. One person believes he may eat anything, while the weak person eats only vegetables. Let not the one who eats despise the one who abstains, and let not the one who abstains pass judgment on the one who eats, for God has welcomed him. Who are you to pass judgment on the servant of another? It is before his own master that he stands or falls. And he will be upheld, for the Lord is able to make him stand" (Romans 14:1-4). In a passage about the weaker brother, Paul tells us that it is not our solicitude for that brother that will keep him from falling. Solicitude is merely the natural outworking of brotherly love. Rather, it is the Lord who keeps him from falling!
The Arminians who hold to eternal security do so for sentimental reasons, not theological. It feels good to be safe for eternity! And I am certainly glad that they have better sense in the sentiment than they do in their theology. However, their sentimentality comes from their failure to understand all that Scripture says about the grace of our sovereign God. I am glad that, when sentiment runs out, I have a sound biblical foundation for my assurance.