Listed below are scriptures and links that speak to causes, cures and strategies for dealing with issues of assurance of salvation:

The work of the Holy Spirit in our lives is to assure us:

Romans 8:16  The Spirit himself bears witness with our spirit that we are children of God,

After remembering the completed work of Jesus on the cross on our behalf, the writer of Hebrews makes clear God’s desire for us is that we live with a growing assurance of our salvation in Christ:

And we desire each one of you to show the same earnestness to have the full assurance of hope until the end, Hebrews 6.11
Let us draw near with a true heart in full assurance of faith, with our hearts sprinkled clean from an evil conscience and our bodies washed with pure water. Let us hold fast the confession of our hope without wavering, for he who promised is faithful. Hebrews 10:22-23

We have an enemy who is working to do just the opposite.  Clear biblical direction for handling Him can be found here.

Hidden sin will over time undermine certainty of salvation as well as our physical health.

Psalms 32:3  For when I kept silent, my bones wasted away through my groaning all day long.
Regularly reading the Bible with the goal of hearing from the Lord will deepen our confidence in our salvation. 
Romans 10:17  So faith comes from hearing, and hearing through the word of Christ.
Staying connected to the church and serving the Lord with others builds our assurance of life in Christ.
1 Corinthians 12:21  The eye cannot say to the hand, “I have no need of you,” nor again the head to the feet, “I have no need of you.”
We can pray for each other and for ourselves that we would better realize who we are and what we have in Christ.
Ephesians 1:18 -19 having the eyes of your hearts enlightened, that you may know what is the hope to which he has called you, what are the riches of his glorious inheritance in the saints, and what is the immeasurable greatness of his power toward us who believe, according to the working of his great might

Ongoing unconfessed and repented of sin will be bring the discipline of our heavenly Father. He is willing to make us miserable. It should not make us doubt that we are his, but rather reinforce that we are His.

Hebrews 12:5-8
5  And have you forgotten the exhortation that addresses you as sons? “My son, do not regard lightly the discipline of the Lord, nor be weary when reproved by him.
6  For the Lord disciplines the one he loves, and chastises every son whom he receives.”
7  It is for discipline that you have to endure. God is treating you as sons. For what son is there whom his father does not discipline?
8  If you are left without discipline, in which all have participated, then you are illegitimate children and not sons.
Micah 7:8-9
8  Rejoice not over me, O my enemy; when I fall, I shall rise; when I sit in darkness, the LORD will be a light to me.
9  I will bear the indignation of the LORD because I have sinned against him, until he pleads my cause and executes judgment for me. He will bring me out to the light; I shall look upon his vindication.
Since our salvation starts in the purposes of God, there is the promise that He will finish what He started. Salvation starts at a point in our past where we first came to be His. It continues in the present as he works to make us more and more like Jesus, a process not completed till we get to heaven. And it is future when he completes His work in us in glory.
What he starts he finishes.
Romans 8:28-30
28  And we know that for those who love God all things work together for good, for those who are called according to his purpose.
29  For those whom he foreknew he also predestined to be conformed to the image of his Son, in order that he might be the firstborn among many brothers.
30  And those whom he predestined he also called, and those whom he called he also justified, and those whom he justified he also glorified.
Philippians 1:6
6  And I am sure of this, that he who began a good work in you will bring it to completion at the day of Jesus Christ.
Jesus said:
John 10:27-29
27  My sheep hear my voice, and I know them, and they follow me.
28  I give them eternal life, and they will never perish, and no one will snatch them out of my hand.
29  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.