I just read a post by Mark Horne in which he said that an Arminian reading of the warning passages of Hebrews does nothing to threaten the monergism of Reformed theology. Though he's not explicit, I assume he means that God monergistically causes some of the non-elect to become Christians for a time, but then God later permits (or causes) them to fall away and go to hell. The eternally elect persevere to the end and inherit eternal life, but not all regenerate, justified, and adopted Christians are eternally elect; therefore, non-eternally-elect Christians always fall away. The reason some Christians persevere and some fall away is because God causes some to persevere, but not all.
I believe that view should be rejected because it calls God's Fatherhood into question and because it runs counter to the teaching of the Bible. The Bible represents God the Father as one who preserves His sons because He loves them. He keeps all His sons to the very end. God never casts off His sons or causes them to fall away. Here are a few passages which teach that God preserves to the end all Christians who are drawn effectually by His power.
Christians Remain Christians to the End
John 6:40 "For this is the will of My Father, that everyone who beholds the Son and believes in Him, may have eternal life; and I Myself will raise him up on the last day."
John 6:44 "No one can come to Me, unless the Father who sent Me draws him; and I will raise him up on the last day."
1 Corinthians 1:7-9 "our Lord Jesus Christ, 8 who shall also confirm you to the end, blameless in the day of our Lord Jesus Christ. 9 God is faithful, through whom you were called into fellowship with His Son, Jesus Christ our Lord."
Philippians 1:6-7 "For I am confident of this very thing, that He who began a good work in you will perfect it until the day of Christ Jesus. 7 For it is only right for me to feel this way about you all, because I have you in my heart, since both in my imprisonment and in the defense and confirmation of the gospel, you all are partakers of grace with me."
1 Thessalonians 5:23-24 "Now may the God of peace Himself sanctify you entirely; and may your spirit and soul and body be preserved complete, without blame at the coming of our Lord Jesus Christ. 24 Faithful is He who calls you, and He also will bring it to pass."
Hebrews 3:14 "For we have become partakers of Christ, if we hold fast the beginning of our assurance firm until the end."
Hebrews 10:14 "For by one offering He has perfected for all time those who are sanctified."
They Were Never Christians in the First Place
In addition to the above passages which teach that those God redeems remain in grace to the end, there are biblical texts that teach that those who fall away from the faith were never actually Christians in the first place.
Matthew 7:21-23 "Not everyone who says to Me, 'Lord, Lord,' will enter the kingdom of heaven; but he who does the will of My Father who is in heaven. 22 "Many will say to Me on that day, 'Lord, Lord, did we not prophesy in Your name, and in Your name cast out demons, and in Your name perform many miracles?' 23 "And then I will declare to them, 'I never knew you; depart from Me, you who practice lawlessness.'"
John 6:64 "But there are some of you who do not believe." For Jesus knew from the beginning who they were who did not believe, and who it was that would betray Him."
1 John 2:19 "They went out from us, but they were not really of us; for if they had been of us, they would have remained with us; but they went out, in order that it might be shown that they all are not of us."